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26 min readβ’june 18, 2024
A Q
A Q
We know that studying for your AP exams can be stressful, but Fiveable has your back! We created a study plan to help you crush your AP Calc BC exam. This guide will continue to update with information about the 2024 exams, as well as helpful resources to help you do your best on test day.Β Unlock Cram ModeΒ for access to our cram eventsβstudents who have successfully passed their AP exams will answer your questions and guide your last-minute studying LIVE! And don't miss out on unlimited access to our database of thousands of practice questions.
Format of the 2024 AP Calculus BC exam
This year, all AP exams will cover all units and essay types. The 2024 Calculus BC exam format will be:
Section 1: Multiple Choice - 50% of your total score
45 questions in 1 hr 45 mins
Part A: 30 questions in 60 minutes (calculator not permitted).
Part B: 15 questions in 45 minutes (graphing calculator required).
Section 2: Free Response - 50% of your total score
6 questions in 1 hr 30 mins
Part A: 2 questions in 30 minutes (graphing calculator required).
Part B: 4 questions in 60 minutes (calculator not permitted).
Check out our study plan below to find resources and tools to prepare for your AP Calculus BC exam.
First, download the AP Calculus BC Cheatsheet PDF - a single sheet that covers everything you need to know at a high level. Take note of your strengths and weaknesses!Β
Review every unit and question type, and focus on the areas that need the most improvement and practice. Weβve put together this plan to help you study between now and May. This will cover all of the units and essay types to prepare you for your exam
Practice problems are your best friends! Both the FRQs and MCQs had several questions that were similar to previous FRQs and the open-sourced multiple-choice questions on College Board (essentially the same questions with different numbers).
We've put together the study plan found below to help you study between now and May. This will cover all of the units and essay types to prepare you for your exam. Pay special attention to the units that you need the most improvement in.
Study, practice, and review for test day with other students during our live cram sessions viaΒ Cram Mode. Cram live streams will teach, review, and practice important topics from AP courses, college admission tests, and college admission topics. These streams are hosted by experienced students who know what you need to succeed.
Before you begin studying, take some time to get organized.
π₯ Create a study space.
Make sure you have a designated place at home to study. Somewhere you can keep all of your materials, where you can focus on learning, and where you are comfortable. Spend some time prepping the space with everything you need and you can even let others in the family know that this is your study space.Β
π Organize your study materials.
Get your notebook, textbook, prep books, or whatever other physical materials you have. Also, create a space for you to keep track of review. Start a new section in your notebook to take notes or start a Google Doc to keep track of your notes. Get yourself set up!
π Plan designated times for studying.
The hardest part about studying from home is sticking to a routine. Decide on one hour every day that you can dedicate to studying. This can be any time of the day, whatever works best for you. Set a timer on your phone for that time and really try to stick to it. The routine will help you stay on track.
π Decide on an accountability plan.
How will you hold yourself accountable to this study plan? You may or may not have a teacher or rules set up to help you stay on track, so you need to set some for yourself. First, set your goal. This could be studying for x number of hours or getting through a unit. Then, create a reward for yourself. If you reach your goal, then x. This will help stay focused!
Unit 1 is the basic idea of all of Calculus. The limit is the concept that makes everything click. You ask someone what they learned in calculus, and they will most likely answer βderivatives and integralsβ. These limits help us to understand what is happening to a function as we approach a specific point. Limits can be one or two-sided, but the sides have to match in order for the limit from both directions to exist! Well without the limit we wouldnβt have either. A major concept used throughout the curriculum and within theorems is continuity. We prove continuity using limits and learn how to do that within this unit. We also learn about the Intermediate Value Theorem and the Squeeze Theorem, although this topic most likely wonβt be directly tested on this yearβs exam, itβs the bread and butter of whatβs to come.Β
Methods of Finding Limits
From a table - Be able to estimate values not given in a table by using values that were given in a table.
From a graph - Be able to use a graph to interpret a limit at an x value.
Algebraically
Limit Properties
Rationalization
Some limits look unsolvable, (0/0 or β/β), but using algebraic manipulation, you can solve them! In unit 4 we learn about another helpful tool for this, LβHospitalβs rule!
Infinite Limits
Squeeze Theorem
The squeeze theorem helps us to find limits of functions that we do not know, by using the limits of a function that is greater than or equal to and a function that is less than or equal to. If we can find the limits of those two functions, and they are equal, then our function should have that limit too!
Continuity and Discontinuity
Students should be able to prove if a function is continuous as a point, and know the different types of discontinuity! Removable, jump, infinite.
First existence theorem: Intermediate Value Theorem
This theorem helps us to prove points that exist given certain information. Donβt forget to always state or prove the conditions! In this case, it would be that the function is continuous on [a, b].
π Read these study guides:
π₯Watch these videos:
Defining Limit and using Limit Notation: Introduction to limits
Graphical Limits: FInding limits given a graph.
Algebraic Limits: How do you find a limit?
Continuity Part I & II: Defining a continuous function
Limits at Infinity: Using limits at infinity to demonstrate function behavior
Working with the Intermediate Value Theorem: There are two theorems that are related to Unit 1: The Intermediate Value Theorem and The Extreme Value Theorem. Learn about the Intermediate Value Theorem here.
Unit 2 introduces the first of the 2 major halves of calculus: differentiation, or the instantaneous rate of change of a function. We start off with defining the derivative and applying it to our old friend, the limit. This unit also sets up the rules so that you can figure out the derivative of the simplest functions you will find on the FRQ section! Derivatives help us determine instantaneous rates of change. We will discuss the difference between average and instantaneous rates of change and how they appear differently. One thing is for sure, you should still follow the order of operations!
Average Rate of Change vs Instantaneous Rate of Change
If we apply a limit to an average rate of change, we are looking at an instantaneous rate of change!
Definition of the Derivative
A long time ago, before we learned the power rule, etc, for the derivative, we learned how to solve the instantaneous rate of change using the limit definition of a derivative.
Estimating The Derivative
Connecting differentiability and continuity. Remember, differentiability implies continuity, but not the other way around! Make sure you know how to tell if a function is differentiable. No cusps or corners, polynomials are always differentiable!
Finding Simple Derivatives
Power Rule
Derivative Properties
Trigonometric Derivatives
Exponential and Logarithmic Derivatives
**While this year it may not be necessary to memorize certain derivatives like natural log or tangent, using time out of your exam time to look them up can be costly! Make sure you are still on your game when it comes to the derivatives you need to know.
Product and Quotient Rules
π Read these study guides:
2.0 Unit 2 Overview
2.1 Defining Average and Instantaneous Rates of Change at a Point
2.2 Defining the Derivative of a Function and Using Derivative Notation
2.4 Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist
2.6 Derivative Rules: Constant, Sum, Difference, and Constant Multiple
2.8 The Product Rule
2.10 Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions
π₯Watch these videos:
The Limit Definition of the Derivative: The derivative from first principles
Introduction to Finding Derivatives: The power rule and trigonometric derivatives, a must-watch!
The Product and Quotient Rules: The product and power rules, a powerful tool in your derivative-finding toolkit!
Practicing Derivative Rules: Applying what youβve learned in finding derivatives so far!
In Unit 3, we expand on the methods of finding derivatives from Unit 2 in order to evaluate any derivative that the Collegeboard can throw at you! This section includes the very important chain rule. Implicit differentiation is a big takeaway from this unit. It allows us to find derivatives of any variable when we may be finding the derivative with respect to something else.
Chain Rule
The chain rule allows us to differentiate composite functions. But make sure you see every function! Sometimes the chain rule can be more than one chain! For example: (sin(x2))2. We have 3 functions to consider here!
Implicit Differentiation
Implicit differentiation gives us the tools to derive any variable with respect to any variable. The main concept is that if the variable you are deriving is not the same as the variable you are taking the derivative of, the chain rule applies and you must also multiply by the derivative of that variable. For example, the derivative of y2with respect to x is 2ydydx.Β
Derivatives of Inverse Functions (Including Trigonometric Functions)
Remember how to find an inverse? Switch x and y and solve for y? Well then take the derivative of that!, or follow the formula we have! The important part to remember on problems like this is the x and y values. If you are supposed to be using the x value of an inverse function, that means it was the y-value of your original function!
π Read these study guides:
3.0 Unit 3 Overview
3.1 The Chain Rule
3.6 Calculating Higher-Order Derivatives
π₯Watch these videos:
The Chain Rule: The chain rule, used to evaluate the derivative of composite functions, very important!
Implicit Derivatives: Derivatives of implicitly defined functions/curves
Practicing Derivative Rules II: Applying what you have learned through the previous 2 units!
Using Tables to Find Derivatives: Finding derivatives when the equation may not be present
Β
Unit 4 allows you to apply the derivative in different contexts, most of which have to do with different rates of change. You will also learn how to solve problems containing multiple rates, how to estimate values of functions, and how to find some limits you may not have known how to solve before! Related rates are a very popular topic in the FRQ section of the exam. It is very important you label every variable you use! Limits you may not have been able to know how to solve before you can now solve using LβHospitalβs rule, but make sure you know the requirements!
Rates of Change
Position, Velocity, Acceleration
Velocity is the derivative of position, and acceleration is the derivative of velocity. Velocity has a direction. If the velocity and acceleration match signs, the particle is speeding up. If their signs are opposite, the particle is slowing down. Speed is the absolute value of velocity and has no direction. On the AP test, you can be asked to map out the path of a particle, which direction it is going, and if it is speeding up or slowing down.
Related Rates
Related Rates have to do with nothing other than relating rates! There are a set of steps to follow when solving a related rate:Β
Linearization and Tangent Line Approximations
In these types of problems, we use a tangent line approximation for one value that we know and use it to approximate another very close value. Let day, x0 is the one we know about, and x1 is the one we need. Then we would use: f(x1)-f(x0)=f'(x0)(x1βx0) to find f(x1).
LβHopitalβs Rule
When using LβHospitalβs rule, we have a few things we need to remember! To apply LβHospitalβs rule, your limit needs to be in one of two forms: 0/0 or β/β. To show this in a free-response question, you need to show the limits in the numerator and the denominator goes to either 0 or infinity separate from each other, then you can use LβHospitalβs rule, which says: xaf(x)g(x)=xaf'(x)g'(x).Β
π Read these study guides:
4.0 Unit 4 Overview
4.2 Straight-Line Motion: Connecting Position, Velocity, and Acceleration
4.6 Approximating Values of a Function Using Local Linearity and Linearization
4.7 Using L'Hopitals Rule for Determining Limits in Indeterminate Forms
π₯Watch this video:
Related Rates: How to solve related rates problems
Unit 5 continues our discussion on the applications of derivatives, this time looking at graphs and how the value of the first and second derivatives of a graph influences its behavior. We will review two of the three existence theorems, the mean and extreme value theorems. Weβll also learn how to solve another type of problem commonly seen in the real world (and also on FRQ problems): optimization problems.
Two of the three Existence Theorems
It is important when using theorems to make sure their conditions are met before you use them!
Mean Value Theorem
In order to use the Mean Value Theorem, the functions must be continuous on a closed interval and differentiable on that same interval, but open. Once you can say for sure that these things are true, the mean value theorem tells us that there must be a point in that interval where the average rate of change equals the instantaneous rate of change, or the derivative, at a point within the interval. f'(c)=f(b)-f(a)b-a.
Extreme Value Theorem
For this existence theorem, the condition is that the function continuous on a finite closed interval. If it is, that means there must be an absolute maximum and an absolute minimum.
Increasing/Decreasing Functions and The First Derivative
If the derivative of a function is positive, then the function is increasing! If the derivative is negative, then the function is decreasing!
Local and Global Extrema
First and Second Derivative Tests for Local Extrema
Candidates Test for Global Extrema
Concavity, Inflection Points, and The Second Derivatives
If the second derivative is positive, the function will be concave up. If the second derivative is negative, the function will be concave down. Whenever the second derivative changes sign, there will be an inflection point, a change in concavity, on the original function.
Curve/Derivative Sketching
All of the information you learned from how the first and second derivatives relate to the original function can help you to sketch graphs based on the information you have about their derivatives!
Optimization Problems
These are also known as applied maximum and minimum problems. These are problems about finding an absolute maximum and an absolute minimum in an applied situation. When trying to find an absolute max or min, you must find all critical points (f'(x)=0 or undefined). Then plug those and the endpoints into the original function to find out which has the highest or lowest value, depending on what you are looking for.
π Read these study guides:
5.0 Unit 5 Overview
5.2 Extreme Value Theorem, Global vs Local Extrema, and Critical Points
5.3 Determining Intervals on Which a Function is Increasing or Decreasing
5.4 Using the First Derivative Test to Determine Relative (Local) Extrema
π₯Watch these videos:
Interpreting Derivatives Through Graphs: Graphical interpretation of derivatives
Existence Theorems: Mean Value Theorem, Extreme Value Theorem, Intermediate Value Theorem
Increasing and Decreasing Functions: Using the first derivative to show where function increases and decreases
Concavity: Using the second derivative to find concavity
f, fβ, and fβ: Relating a function and itsΒ
Optimization Problems: How to solve optimization problems
Unit 6 introduces us to the integral! We will learn about the integral first as terms of an area and Reimann sums, then working into the fundamental theorem of calculus and the integral's relationship with the derivative. We will learn about the definite integral and the indefinite integral. We learned about methods of integration from basic rules to substitution. In BC, there are also the methods of integration by parts, partial fractions, and improper integrals. In some cases, the integral is called the antiderivative, and if f is the function, then F would be the antiderivative of that function.
Approximating an integral as an area
When given a graph, we can find the area under the curve and between the x-axis to find the integral. However, if an area is underneath the x-axis, that would be considered negative.
Riemann Sums
A way of evaluating an area under a curve by making rectangles to find the area and adding them up. This is useful with a table of values or with a curve that we do not know the exact area of its shape. There are four kinds: Left, Right, Midpoint, and Trapezoidal sum. Depending on the function, these may be over or underestimates of the actual area.Β
Students should also be able to write a Reimann sum in summation notation and integral notation.
The Fundamental Theorem of Calculus
This theorem tells us two very important things:Β
abf(x)dx=F(b)-F(a)
ddx(axf(t)dt)=f(x), where a is a constant.
We use this theorem very often when working with integrals.Β
Definite vs. Indefinite Integrals
Integrals must always include a dx (if not x, whichever variable you are using) at the end.Β
If an integral is indefinite, it has no bounds. This means it cannot be evaluated using the fundamental theorem of calculus. Instead, we add on a +C, to make it know that there could have been a constant at the end of the function and that there are lots of possibilities for what that constant would be.Β
Definite integrals have bounds, and we use the fundamental theorem of calculus often with them. The bounds let us know the endpoints of the integral, or in terms of a graph, what two points we are finding the area under the curve between.Β
Integral Rules
Make sure you remember how to integrate and its connection to deriving!
You can check an integral by taking its derivative to see if you get back to where you started.Β
U-Substitution
When you have a composition of functions in an integral, it is necessary to use u-substitution to make sure you are integrating each part. It is usually the inside function that is chosen. Sometimes it can be hard to tell. You will know once you try! If you find yourself going in circles and needing to substitute more, I would try using a different piece of the function as u.Β
Integrating using integration by parts
Integration by parts you can use when you are multiplying two functions, it looks like this:
udv=uv-vdu.
When trying to figure out which function to prioritize as u, make sure to go to this helpful order:
LIPET (Logs, Inverse Trig, Polynomials, Exponentials, Trig). Whichever one appears first, use that for u, then use the other for dv. Find du and v, and plug-in from there!
Integrating using partial fraction decomposition
This is helpful when dealing with a rational function in your integral. The denominator should be a higher power than the numerator to use this. It helps turn terms into sums of ratios of linear nonrepeating decimals that are integrable.Β
Evaluating Improper Integrals
An improper integral has one or both limits at infinity. In order to integrate these, we denote that infinite bound as a variable, a, and take the limit as a approaches infinity of the integral of our function. The fundamental theorem of calculus really helps us here!
π Read these study guides:
6.0 Unit 6 Overview
6.12 Using Linear Partial Fractions
π₯Watch these videos:
The Fundamental Theorem of Calculus: Explains the Fundamental Theorem of Calculus and its uses as the most important theorem in calculus
Some Integration Techniques: How to do integration techniques found in Calculus AB
Unit 7 takes us to a great connection between integrals and derivatives in differential equations. We will learn how to model and solve differential equations using initial conditions. This always requires the separation of variables when it comes to free-response questions! We will also learn how to identify differential equations from their slope fields and how to draw those fields as well. BC Calculus adds in Eulerβs method and logistic models in this unit.Β
Differential Equations
Modeling
If you are given information, can you write a differential equation from it?Β
Verifying Solutions
Being able to plug in given information and deduce if the solution is true.Β
Separation of variables
This often appears in the FRQ section. Students are given a differential equation and need to put all of the terms for one variable on one side and for the other variable on the other, then they integrate both sides and solve for y, usually y, but really whichever the dependent variable it.Β
NOTE: If you skip the step of separating variables on AP exams in the past, they have offered you no credit for the rest of that section of the problem.Β
Using initial conditions
Once you have done your separation of variables, donβt forget to have a +C! This is where the initial condition comes in. You plug in the terms given from x and y in your initial condition, then you solve for C, rewriting the function at the end with C plugged in!
Slope fields
Slope fields are coordinate planes of 1 by 1 sections of slopes at each x and y value. If given a differential equation and asked to find a slope field, you plug in an x and y pair into the differential equation, the value it outputs is the slope at the point, and is the steepness you used to draw a line at that particular pair.Β
Eulerβs Method
This is another method for approximating a solution to a differential equation or a point on a solution curve.Β
Logistic Models with Differential Equations
This is a joint proportional differential equation. dy/dt=ky(a-y). You can interpret the initial condition and the differential equation without solving the differential equation.Β
The limiting value, also known as the carrying capacity, can be determined using a logistic growth model.Β
The logistic growth model can also be used to determine the value of the dependent variable in the logistic differential equation at the point when it is changing the fastest.Β
π Read these study guides:
7.0 Unit 7 Overview
7.7 Finding Particular Solutions Using Initial Conditions and Separation of Variables
π₯Watch this video:
Separable Differential Equations: How to solve separable differential equations
Unit 8 teaches us more useful applications of the integral as we enter the 3D graph world! We learn how to find the average value of a function and the particle motion according to an integral. BC Calculus also adds in the arc length here! We also use cross-sections and disks and washers to find the volume of shapes as functions are revolved around either a vertical or horizontal line. We put our spatial reasoning and geometry skills to use in this section.Β
Average Value of a function
The average value of a function is denoted by 1b-aabf(x)dx. We can only find the average value of a function that we have a definite integral for.Β
Position, Velocity, Acceleration
Position is the integral of velocity, and velocity is the integral of acceleration! If you take the absolute value of velocity, you are able to find speed.Β
Distance, the integral of the absolute value of velocity
Displacement, the integral of velocity
To remember this, I think about a track! After one lap around, your distance is 400Β m, but your displacement is 0. Make sure if you are asked for distance, you remember to use absolute value!
Finding the area between curves
If given two curves on a coordinate plane and endpoints, students should be able to integrate those functions, either with respect to the x or y-axis, in order to determine the area between them. When talking about the x-axis, all functions should be in terms of x, the bounds should be in terms of x, and it will be the integral of the upper functions minus the lower. When talking about with respect to the y-axis, all functions should be in terms of y, the bounds should be in terms of y, and it will be an integral of an outer function minus the inner.
Finding the area between curves that intersect at more than two points.Β
Sometimes, your function will have different parts where you may need to split the area and add your answers together, because the upper functions changes or another function changes.Β
When in doubt, break it up into pieces, you know how to work with, and add those together.Β
The area under the x-axis is already accounted for as negative when evaluating using an integral, so donβt worry about that!
Volumes of cross-sections
When using cross-sections, you integrate the area of whatever shape is given to you (this could be a square, rectangle, triangle, or semicircle).Β
You will integrate the area on a given interval, but it is important that you interpret the function for the variable in the shape that it represents.Β
If it says perpendicular to the x-axis, all should be in terms of x.
Perpendicular to the y-axis, all should be in terms of y.Β
Volumes by disks and washers
In this case, we are integrating an area again, but this time the shape will always be a circle, so we will always be using the area formula for a circle. The variable that changes here is r, the radius, which you can interpret using the function.Β
If the rotation is around just the x-axis, all should be in terms of x (bounds and functions) and the radius will be your function.Β
If the rotation is around just the y-axis, all should be in terms of y (bounds and functions) and the radius will be your function.
If it is rotated around any other vertical or horizontal line, you may need to add or subtract value from your function to find the radius.Β
A washer is when two functions are used, and you must subtract out the volume the inner function would have added into your total volume to account for the missing piece.Β
Arc Length
BC Students are also required to know how to find the arc length of a smooth, planar curve and distance traveled.Β
A definite integral can be used to calculate this. s(x)=ax1+[f'(t)]2dt.Β
π Read these study guides:
8.0 Unit 8 Overview
8.2 Connecting Position, Velocity, and Acceleration of Functions Using Integrals
8.3 Using Accumulation Functions and Definite Integrals in Applied Contexts
8.4 Finding the Area Between Curves Expressed as Functions of x
8.5 Finding the Area Between Curves Expressed as Functions of y
8.6 Finding the Area Between Curves That Intersect at More Than Two Points
8.9 Volume with Disc Method: Revolving Around the x- or y-Axis
8.11 Volume with Washer Method: Revolving Around the x- or y-Axis
π₯Watch these videos:
Interpreting the Meaning of the Derivative and the Integral: Showing derivatives and integrals applied in different contexts
Position, Velocity, and Acceleration: Exploring the relationship between position, velocity, and acceleration
Unit 9 is only BC, and weβll learn about parametric functions and polar functions. Weβll be expected to solve parametrically defined functions, vector-valued functions, and polar curves using applied knowledge of differentiation and integration.Β
9.1: Defining and Differentiating Parametric Equations
Parametric functions are a set of related functions where x and y are independent of each other but connected using the variable t.
x(t)=t^2-1, y(t)=3t
To find the slope of the tangent line, we need to find dy/dx
9.4 Defining and Differentiating Vector-Valued Functions
Parametric functions are associated with time and are generally used to calculate motion and velocity.
Each point on a vector-valued function is determined by a position vector, a vector that starts at the origin.
Vector-valued functions tell us how much the particle is moving in the direction of x and how much it is moving in the direction of y.
9.7: Defining Polar Coordinates and Differentiating in Polar FormΒ
Polar functions are functions that are graphed around a pole in a circular system and with the points (r, theta) instead of (x, y).
The slope of the tangent lines for polar functions can be found using the formula dy/dx = (rcos(theta)+(dx/d(theta))sin(theta))/(-rsin(theta)+cos(theta)(dx/d(theta))
9.9: Finding the Area of the Region Bounded by Two Polar Curves
To find the area between two curves, you subtract βouter minus innerβ.
Arc length for polar functions can be found using the formula
π Read these study guides:
9.0 Unit 9 Overview
9.3 Finding Arc Lengths of Curves Given by Parametric Equations
9.6 Solving Motion Problems Using Parametric and Vector-Valued Functions
9.7 Defining Polar Coordinates and Differentiating in Polar Form
9.8 Find the Area of a Polar Region or the Area Bounded by a Single Polar Curve
9.9 Finding the Area of the Region Bounded by Two Polar Curves
Unit 10 is only BC and covers many topics under the umbrella of sequences and series. We learn how series can diverge or diverge and how to know. We learn many different types of convergence tests along with many different types of series! This year some sections have been taken out to account for what you may have learned so far in class. We outline those specific sections to focus on below.Β
10.2: Working with geometric series
A geometric series has a constant ratio between successive terms.Β
n=0arn=a1-r, and r>0
If r<1, then the series converges but diverges otherwise.Β
10.5 Harmonic Series and p-series
This section includes the harmonic series, the alternating harmonic series, and the p-series.Β
The harmonic series is a divergent infinite series. k=11k. This form should be familiar to you.Β
The alternating harmonic series converges conditionally. k=1(-1)k-1k because this series converges, but the absolute value of its series, the harmonic series, does not.Β
P series is any series in the form n=101np. If p is greater than 1, it converges. Otherwise, it diverges!
10.7: Alternating series test for convergence
An alternating series is one that changes sign, so it is in the form an=(-1)n+1bn where bn>0 for all n and bn is decreasing, and nbn =0, then n=1an converges.
This means you need to find nbn. If it is zero and all of the other conditions are met, you have a convergent series.Β
10.8: Ratio Test for Convergence
The ratio test compares a term from the series to a different value in the series by taking its limit.
If our series is and then to use the ratio test, we want to find L, where L=nan+1an. If L < 1, the series is absolutely convergent. If L > 1, the series is divergent, if L=1, we have more work to do, because the series could still be divergent, conditionally convergent, or absolutely convergent.Β
NOTE: These are the only tests for convergence that are on the AP exam. If asked explicitly to use them, you should! If you are told to figure out whether a series is convergent or not and not given a specific method, feel free to use another method you learned even if it is not on the test.Β
10.11: Finding Taylor Polynomial Approximation of Functions
A Taylor polynomial centered at x=a can be found using this form:
f(x)=f(a)+f'(a)(x-a)+fβ(a)(x-a)22!+fβ'(a)(x-a)33!+β¦..+f(n)(a)(x-a)nn!.Β
These Taylor polynomials can be used to approximate function values near x=a.Β
The more terms you find in an nth degree Taylor polynomial, the closer you are to approximating the actual function.
π Read these study guides:
10.0 Unit 10 Overview
10.12 Lagrange Error Bound
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