Texts:
A. A cylindrical tank with a radius of 5m is, at this moment, being filled with water at a rate of 3 m^3/min. How fast is the height of the water increasing? Include units.
B. Before hitting the ceiling, the height of a ball thrown directly upwards in a large gymnasium is given by the function s(t) = -16t^2 + 64t + 6, where s is the height of the ball above the ground, in feet, and t is the time after release, in seconds. The ceiling is 54 feet above the ground. What is the velocity of the ball when it hits the ceiling? Simplify and include units.
Find dy/dx by implicit differentiation: x^2 - 4xy + y^2 = 4
Prove the formula for d/dx [arccos x] in the same manner used for d/dx [arcsin x] in class.
Find the equation of the tangent line to the curve y = 2xe^x at the point (0, 0).