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 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 = x² 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 = sin²3t + cos 3t