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EGET 3171

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**Derivatives of Logarithmic and Trigonometric Functions**

1. The radius of a spherical balloon depends on time according to the function: r = 1 + ln (t), where r is in inches. Find the rate of change of the volume of the balloon after 10 seconds. (13.71 inches)

2. The income from selling x items per week is: I = 50xe

^{-x/10}. How many items must be sold in order to maximize income? (10)

3. Two sides of a triangle are 15 and 20 feet long. How fast is the third side increasing in length when the angle between the given sides is 60

^{o}and is increasing at a rate of 2^{o }per second? (0.503ft/sec)

4. Find the minimum and maximum points for the curve: y = x

^{2}e^{x}. (0.0541)

5. A weight connected to a spring moves so that its displacement in centimeters is a function of time in seconds:

x = sin

^{2}3t + cos 3t

What is the maximum displacement of the weight? (1.25 cm.)