Calculus Answers

A ball is thrown vertically upward from the ground with an initial velocity of 64 ft/sec. If the positive direction of the distance from the starting point is up,

the equation of the motion is s =-16t²+64t. Let t seconds be the time that has elapsed since the ball

was thrown and s feet be the distance of the ball from the starting point at t seconds.

A. Find the instantaneous velocity of the ball at the end of 1 sec. Is the ball rising or talling at the end of 1 sec?

B. Find the instantaneous velocity of the ball at the end of 3 sec. Is the ball rising or falling at the end of 3 sec?

C. How many seconds does it take the ball to reach its highest point?

D. How high will the ball go?

E. Find the speed of the ball at the end of 1 sec and 3 sec.

F. How many seconds does it take the ball to reach the ground?

G. Find the instantaneous velocity of the ball when it reaches the ground.

An object falls from rest, and s =-16t² where s feet is the distance of the object from the starting point at t seconds, and the positive direction is upward. If a stone is dropped from a building 256 ft high, find

A. the instantaneous velocity of the tone 1 sec after it is dropped;

B. the instantaneous velocity of the stone 2 sec after it is dropped;

C. how long it takes the stone to reach the ground;

D. the instantaneous velocity ot the stone when it reaches the ground.

Given a series 1 + 1/2 + 1/4 + 1/8 + 1/16+......; determine the nature of the series, the sum of the n term of the series and sim of the terms as n tends to infinity.

a)Find the antiderivative for sec(x)tan(x)dx

b)Given: integral from 0 to pi sec(x)+tan(x)dx-->If you found an antiderivative in part (a), explain why the result for the definite integral using the same function is undefined.

Find f'(x) of f(x)= sin{x/(x - sin[x/(x-sinx)])}

Find f'(x) of f(x)= 1/{x-[2/(x + sinx)]}

Find f'(x) of [sinx².sin²x]/(1 + sinx)

Find f'(x) of f(x)= sin[(sin⁷x⁷ + 1)⁷]

Find f'(x) of f(x)= sin²x.sinx².sin²x²

Find f' in terms of g' of f(x)=g(x)(x-a)