Calculus Homework

Q: Suppose we are pumping air into a spherical balloon at a rate of 50π ft3 per minute. How fast is the balloon’s diameter increasing at the instant the radius is 5 ft? How fast is the surface area increasing?

Q: - Find equations for the tangent and normal to the equation y2(2 − x) = x3 at (1, 1)

Q: Assume that a particle’s position on x-axis is given by

x = 3 cost + 4 sin t 

where x is measured in feet and t is measured in seconds.

(a) Find the particle’s position when t = 0, t = π/2, and t = π

(b) Find the particles velocity when t = 0, t = π/2, t = π 

(c) Do the same with speed and acceleration.

Q: Find all points (x, y) on the graph of y=x/x-2 with tangent lines orthogonal (perpendicular) to the line y = 2x – 3.