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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
