Free Educational Material (28 Practice Problems)

AP Calculus: AB

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f(-2) = -5

All reals

all x not equal to 0, 1

It is 2 because g(x) is always 2 (constant).

2^3 -3(2^2) -2*2 + 5 = -3

x^3 + 1

1/2 and -1

x + 2 = sqrt(4x), x + 2 = 2 * sqrt(x), (x+2)^2 = 4x, so x^2 + 4x + 4-4x = 0, so x^2 + 4x = 0 so x^2 = -4x which means they don't intersect.

x since for an inverse function, inserting it as an argument into the original function and vice versa always returns x.

3 * pi / 2

-1

nonexistent

5x^4 * tan(x) + x^5 * sec^2(x)

(-(3x+1) - 3*(2-x)) / (3x+1)^2

(((e^x - 1) / (e^x)) * (e^x - 1)/x - (e^x / x)) / (e^x - 1)^2

(sec x tan x + sec^2 (x)) / (sec x + tan x)

cos(1/x) (-x^(-2))

e^(-x) -2sin(2x) -e^-x * cos(2x)

y' = 8*x^(-1/2), so y'' = -4x^(-3/2)

2x + 2yy' = 0, so x + yy' = 0, y' = -y/x

Infinity

cos(xy)*(xy' + y) = 1, solve for y'.

3y^2y' - (x2yy' + y^2) = 0, so at y = 2, y' = 1/2

-xe^-x

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Carnegie Mellon University

AP Calculus: AB Tutor

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Free Educational Material (28 Practice Problems)

AP Calculus: AB

Answer the following without using your calculator: If f(x) = x^3 - 2x - 1, what is f(-2)?

Answer the following without using your calculator: If f(x) = x^3 - 2x - 1, what is f(-2)?

The domain of f(x) = (x - 1) / (x^2 + 1) is

The domain of g(x) = (sqrt(x - 2)) / (x^2 - x) is

If f(x) = x^3 - 3x^2 - 2x + 5 and g(x) = 2, what is g(f(x))?

If f(x) = x^3 - 3x^2 - 2x + 5 and g(x) = 2, what is f(g(x))?

Which of the following functions is not odd? f(x) = sin(x), g(x) = sin(2x), h(x) = x^3 + 1

The roots of equation f(x) = 0 are 1 and -2. What are the roots of f(2x) = 0?

The values of x for which the graphs of y = x + 2 and y^2 = 4x intersect are

Let f(x) have an inverse function g(x). Then f(g(x)) = ?

The smallest positive x for which the function f(x) = sin(x/3) - 1 is a maximum is

lim (x^2 - 4) / (x^2 + 4) as x-> 2 equals?

lim (4 - x^2) / (x^2 - 1) as x-> infinity equals?

lim (x/x) as x-> 0 equals?

lim sin(1/x) as x-> 0 equals?

lim abs(x)/x as x-> 0 equals?

If y = x^5 * tan(x), what is y' ?

If y = (2-x) / (3x + 1), what is y' ?

If y = ln (e^x / (e^x -1), what is y' ?

If y = ln (sec x + tan x), what is y' ?

If y = sin(1/x), what is y' ?

If y = e^-x cos(2x), what is y' ?

If y = 16 sqrt(x), what is y'' ?

If x^2 + y^2 = 25 what is y'?

What is lim (e^x / x^50) as x->infinity?

If sin(x*y) = x

The slope of the curve y^3 -xy^2 = 4 at the point where y = 2 is

The tangent to the curve of y=xe^-x is horizontal when x is equal to

Vasilios S.