1

## Question

1. (8 points) Let r(0) = k tan o be a curve defined in polar coordinates, where k is a nonzero real constant. Find the correct formula for " dy dx
2. (10 points) Given below are the graphs of two functions y = f(x) and y = g(x). Use the graphs to find the indicated value. y = f(x) y = g(x) WN Find the correct value for h'(0) where h(x) = g(x) arctan (f(x)). 3. (8 points) Consider the parametric equations x = 3a cos 2t and y = 3b sin 4t, where a and b are nonzero real dy constants. What is the correct value of ? dxl.
(r? -4 4. (10 points) Use logarithmic differentiation to find p'(x) where p(x) = - 5)' Vx (x* – 8x) 9 5. (8 points) A plane takes off from an airport located at sea level and its altitude (in feet) after t minutes is given by h= f(t)=1500d In(2t + 1) +mt+b, where 0575100 and d, m, and b are all positive real constants. Determine how fast the plane is rising after 3 minutes. Give a 3 decimal approximation.
6. (16 points) Water is leaking out of an inverted conical (base at the top) tank at a rate of 10,000 cm/min at the same time that water is being pumped into the tank at a constant rate. The tank has height 6 meters and the diameter at the top is 4 meters. If the water level is rising at a rate of 20 cm/min when the height of the water is 2 meters, find the rate at which is the water is being pumped into the tank. You must draw a diagram modeling the situation and show all work in an organized matter to receive full credit.

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