AP Calculus BC Problems with Solutions

Problem 1 :

Given :

Evaluate :

Solution :

Problem 2 :

If f(x) = 2^{tan x}, than f'(π/4) =

A)  ln 4

B)  ln 8

C)  ln 16

D)  ln 32

Solution :

Problem 3 :

The above piece-wise function f(x) is continuous on (-∞, ∞), what is the value of a?

A)  7

B)  5

C)  3

D)  1

Solution :

Problem 4 :

If four sub equal subdivisions are used for the interval [1, 2], what is the trapezoidal approximation of the following definite integral?

Solution :

Problem 5 :

A)  tan⁴ x

B)  sec² x + tan² x

C)  sec² x - sec x tan x

D)  tan³ x sec x

Solution :

Problem 6 :

Let f be the function defined by f(x) = e^xcos x. Let g be a differentiable function such that g(π/2) = 0. The graph of g', the derivative of g, is shown below. Find the value of lim(x---> π/2) f(x)/g(x) or state that it does not exist. Justify your answer.

Solution :

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