final review 2 - iowa state university · 2016. 4. 28. · worksheet: final review 2 session 39...

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1. Find all values of the constants a and b for which the function is defined by below is

continuous.

𝑓 𝑥 =𝑥! + 𝑎𝑥 + 𝑏, 𝑥 ≤ 1

𝑥! − 3𝑥 + 2, 1 < 𝑥 ≤ 1𝑥! + 𝑎𝑥 + 𝑏, 𝑥 > 3

2. Find the vertical and horizontal asymptotes for the following functions.

a. 𝑓 𝑥 = !!!!

!!!!!!!

b. 𝑓 𝑥 = !!

!!!!!!!!!

3. Find the derivative of the following functions.

a. 𝑓 𝑥 = 𝑥! sin!!(𝑥)+ log!" 𝑒! + 2𝑥! − sin!

!!!!

b. cos 𝑦 − 4! + 𝑥𝑦! = tan!!(𝑥)

c. 𝑓 𝑥 = !!! !!!!!!!

!!!!!! !!! !

4. Perform the first and second derivative test for 𝑓 𝑥 = 𝑥! 𝑥 − 2 !.

5. Find the linear approximation of 2! .

6. A sailboat 3 miles west of Point A sails towards the Point at 4 miles per hour. At the same moment, a motorboat 4 miles north of Point A travels south towards the Point at 12 miles per hour. After 1 hour, what is the rate of change in the distance between the sailboat and motorboat?

7. A sphere was measured and its radius was found to be 45 inches with a possible error of no more than 0.01 inches. What is the maximum possible error in the volume?

8. A manufacturer needs to make a cylindrical can that will hold 1.5 L of liquid. Determine the dimensions of the can that will minimize the amount of material used in its construction.

Worksheet: Final Review 2 Session 39 Supplemental Instruction Iowa State University

Leader: Zach A Course: Math 165

Date: April 28th, 2016