Questions from General Calculus

Q: Find f (x). f"(x) = 1

Find f (x). f"(x) = 1 - 6x + 48x2 f (0) = 1 f'(0) = 2

Q: Find f (x). f"(x) = 2x3

Find f (x). f"(x) = 2x3 + 3x2 - 4x + 5 f (0) = 2, f(1) = 0

Q: A particle is moving with the given data. Find the position

A particle is moving with the given data. Find the position of the particle. v (t) = 2t – 1/ (1 + t2), s (0) = 1

Q: Find the volume of the solid obtained by rotating the region bounded

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.

Q: Show that if f is a polynomial of degree 3 or lower

Show that if f is a polynomial of degree 3 or lower, then Simpson’s Rule gives the exact value of fba f (x) dx.

Q: A particle is moving with the given data. Find the position

A particle is moving with the given data. Find the position of the particle. a (t) = sin t + 3 cos t, s (0) = 0 v (0) = 2

Q: Determine whether the statement is true or false. If it is

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. 1. If f'(c) = 0, then f has a local maximum o...

Q: Find the local and absolute extreme values of the function on the

Find the local and absolute extreme values of the function on the given interval.

Q: Sketch the graph of a continuous, even function f such that

Sketch the graph of a continuous, even function f such that f (0) =, f'(x) = 2x if 0 < x < 1, f'(x) = -1 if 1 < x < 3, and f'(x) = 1 if x > 3.

Q: A canister is dropped from a helicopter 500 m above the ground

A canister is dropped from a helicopter 500 m above the ground. Its parachute does not open, but the canister has been designed to withstand an impact velocity of 100 m/s. Will it burst?