EGET 3171


EGET 3171

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 60o and is increasing at a rate of 2o per second? (0.503ft/sec)


4. Find the minimum and maximum points for the curve: y = x2 ex. (0.0541)


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

x = sin23t + cos 3t

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