MATH 124 Study Guide - Final Guide: Atan2, Radian
1 Oct 2018
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Math 124 Final Examination AUTUMN 2012
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!!! READ...INSTRUCTIONS...READ !!!
1. Your exam contains 9 questions and 12 pages; PLEASE MAKE SURE YOU HAVE A COM-
PLETE EXAM.
2. The entire exam is worth 100 points. Point values for problems vary and these are clearly
indicated. You have 2 hours and 50 minutes for this final exam.
3. Make sure to ALWAYS SHOW YOUR WORK; you will not receive any partial credit unless
all work is clearly shown. If in doubt, ask for clarification.
4. There is plenty of space on the exam to do your work. If you need extra space, use the back
pages of the exam and clearly indicate this.
5. You are allowed one 8.5×11 sheet of handwritten notes (both sides). Graphing calculators
are NOT allowed; scientific calculators are allowed. Make sure your calculator is in radian
mode.
Problem Total Points Score
1 12
2 12
3 12
4 13
Problem Total Points Score
5 8
6 15
7 6
8 10
9 12
Total 100
1
1. (12 points; 4pts each) Find the derivatives of the following functions. You do not have
to simplify. Your final answers must give the derivative in terms of x.
(a) f(x) = qx+ sin(x+√x)
(b) y= (1 + x)cos x
(c) y= arctan 1
2 + x2
2
2. (12 points) A pump with a constant flow rate is filling a spherical balloon with water.
The balloon expands as more water enters. When the balloon’s radius reaches 10 cm,
it is increasing at a rate of 0.5 cm/minute. (Recall that for a sphere of radius r, the volume
is given by the formula: V=4
3πr3.)
(a) What is the flow rate, in cm3/min?
(b) How long has it been since the pump started filling the empty balloon?
(c) Five minutes later, is the radius increasing at a rate faster or slower than 4
cm/minute. Give a reason.
3
Document Summary
Readinstructionsread !: your exam contains 9 questions and 12 pages; please make sure you have a com- Plete exam: the entire exam is worth 100 points. Point values for problems vary and these are clearly indicated. You have 2 hours and 50 minutes for this nal exam: make sure to always show your work; you will not receive any partial credit unless all work is clearly shown. If in doubt, ask for clari cation: there is plenty of space on the exam to do your work. If you need extra space, use the back pages of the exam and clearly indicate this: you are allowed one 8. 5 11 sheet of handwritten notes (both sides). Graphing calculators are not allowed; scienti c calculators are allowed. Make sure your calculator is in radian mode. 1: (12 points; 4pts each) find the derivatives of the following functions.
