AP Calculus Cheat Sheet



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AP Calculus Concept Checklist

POINTS TO REMEMBER

To find the average rate of change: Find the slope of the points

Instantaneous Rate of Change : Find the Slope of Tangent Line i.e. find the derivative and substitute the given points

LIMITS AND CONTINUITY

Limits:

1. When finding limits at a number, try plugging number in first.

2. If that doesn’t work, try factoring, using common denominators, or using conjugates.

3. Left and right sided limits must be equal for limit to exist.

4. Limit approaching infinity, apply the three conditions for the degree of numerator and denominator

5. Limits from graph: Look if the limit from the left equals the limit from the right. Check if there are any breaks in the graph

Limits and Continuity:

A function [pic] is continuous at [pic] if

i). f(a) exists

ii). [pic] exists

iii). [pic]

Otherwise, f is discontinuous at x = a.

The limit [pic] exists if and only if both corresponding one-sided limits exist and are equal – that is,

[pic]

Limits of Rational Functions as [pic](Similar to Horizontal Asymptote)

i). if the degree of [pic] Example: [pic]

ii). if the degrees of [pic] Example: [pic]

iii). if the degree of [pic] Example: [pic]

DERIVATIVES

FORMULA

1. [pic] Remember:

2. Product Rule [pic] 1. Rewrite radicals as exponents

3. Quotient Rule [pic] 2. Use laws of exponents

4. [pic]

5. [pic]

6. [pic]

7. [pic]

8. [pic]

9. [pic]

10. [pic]

11. [pic]

12. [pic]

13. [pic]

14. [pic]

15. [pic] finds the derivative of [pic] at x. This WILL BE a multiple choice question.

Chain rule:

1. Derivative of the outside function times the derivative of the inside function

2. Remember the short cut for trig, ln, e

Implicit derivative:

1. When differentiating y, remember to write the dy/dx

2. The aim is to get dy/dx on one side and the other terms on the right

Steps to find the equation of the tangent:

1. Find the derivative

2. Substitute the given points to find the slope

3. Use point slope form to find the equation

Critical number: Set the first derivative equal to zero

1st Derivative Test:

1. Tells us max/min,

2. Tells us increasing/decreasing intervals

3. Tells us slope of a tangent line

4. Can be used to find velocity.

Point of inflection: Set the second derivative equal to zero

2nd Derivative Test(Concavity)

1. Tells us inflection points

2. Tells us about the concavity (>0 is concave up, ................
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