Quiz #7

Sections 3.11, 4.1, 4.3, 4.4 and pages 267, 269 and 273

20 points (5 points each)

You have 25 minutes for this quiz. You MUST show work for credit. You must use the methods we have covered.

1. Find the limit using l'Hospital's Rule.

a.

b.

2. A paper cup has the shape of a cone with height 10 cm and radius 3 cm (at the top). If water is poured into the cup at a rate of 2 , how fast is the water level rising when the water is 5 cm deep?

PLEASE, TURN THE PAGE OVER!

3. Given the following function: , use the First and Second Derivative tests as appropriate to answer the questions.

a. Find the intervals on which f(x) is increasing or decreasing.

b. Find the local maxima and minima values of f(x).

c. Find the intervals of concavity and any inflection points.

4. Given the curve ,

a. Find the equation for the distance from the Origin to a point (x,y) on the curve. Write the equation as a function of x.

b. Find the linearization, L(x), of the distance formula at a = 4.

c. Use this to approximate the distance at x = 3.9