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 athlete doing agility training starts at point A and runs to point B and then turns and runs back to point A and turns again and runs back to point B. The position for the athlete at time t is given by

𝑠(𝑡) = 𝑡³ − 6𝑡² + 9𝑡 − 2

1. On which intervals is the velocity positive? In which direction is the athlete running during these

time intervals?

2. On which intervals is the velocity negative? In which direction is the athlete running during these

time intervals?

3. At which points is velocity zero? What is the athlete’s movement at these points?

Prove that of all rectangles with given perimeter, the square has the greatest area.

If a1< ...... <an . Find the minimum value of f(x) = (x - ai)² summation from i=1 to n

Draw a graph of the displacement y (m) against time t(s) for the time

between to

a)   Draw a graph of the displacement y(m) against time t(s) for the time  t=0s to t=2s

Find all second order partial derivatives of f. And verify whether fxy=fyx at any (x,y) for each f. F(x,y)=y cos x-e×

The inverse demand function is given by P = 2 – 0.13 Q.

What is the price elasticity of demand?

What is the price elasticity of demand when P = 1.2

Prove that the vector A = 3yz2 i + 4x322 j - 3x2y2 k is solenoidal

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.