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Study Guide for the AP Calculus AB exam

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Transcript of Study Guide for the AP Calculus AB exam

AP Calculus AB Study Guide
By: "Lew" Sterling Jr.
All of the baggage
has to be checked
before it is loaded.
What the AP Calculus AB will be about:
Elementary Functions
Limits
Differential Calculus
Integral Calculus
Elementary
Functions
Properties of Functions
Combinations of
Functions
Inverse
Functions
Even and Odd Functions
The function y = ƒ(x) is even if ƒ(-x) = ƒ(x).
Even functions are symmetric about the y-axis (e.g. y = x^2)

The function y = ƒ(x) is odd if ƒ(-x) = -ƒ(x).
Odd functions are symmetric about the origin (e.g. y = x^3)
Periodic
Functions
Zeros of
a Function
These occur where the function ƒ(x) crosses the x-axis. These points are also called the roots of a function.
Limits
A limit is the value that a function or sequence "approaches" as the input or index approaches some value. Limits are essential to calculus (and mathematical analysis in general) and are used to define continuity, derivatives, and integrals.
One last thing you need to know before Differential Calculus...
Properties of Limits
and One-Sided Limits
Limits at Infinity
Intermediate Value Theorem
Differential Calculus
Differentiation Rules
Mobile X-rays are large truck carriers that has a complex X-ray system.
Example of
Differentiating
CT scanner mechanism
In the United States, most major airports have a computer tomography (CT) scanner.
The CT scanner rotates around the bag, bombarding it with X-rays and recording the resulting data, creating a tomographic.
Not all baggages go through a CT scan
Usuallylocated near the ticket counter.
A function ƒ is defined as a set of all ordered pairs (x, y), such that for each element x, there corresponds exactly one element y.
The domain of ƒ is the set x.
The range of ƒ is the set y.
If ƒ(x) = 3x + 1 and g(x) = x^2 - 1

a) the sum ƒ(x) + g(x) =
(3x + 1) + (x^2 - 1) = x^2 + 3x

b) the difference ƒ(x) - g(x) =
(3x + 1) - (x^2 - 1) = -x^2 + 3x + 2

c) the product ƒ(x)g(x) =
(3x + 1)(x^2 - 1) = 3x^3 + x^2 - 3x - 1

d) the quotient ƒ(x)/g(x) =
(3x + 1)/(x^2 - 1)

e) the composite (ƒ * g)(x) = ƒ(g(x)) =
3(x^2 - 1) + 1 = 3x^2 - 2
Functions ƒ and g are inverses of each other if
ƒ(g(x)) = x

for each x in the domain of g
g(ƒ(x)) = x

for each x in the domain of ƒ

The inverse of the function ƒ is denoted ƒ-1.

To find ƒ-1, switch x and y in the original equation and solve the equation for y in terms of x.
You should be familiar with the definitions and graphs of these trigonometric functions:
sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc)
Full transcript