Department

Applied MathCourse Code

APPM 1350Professor

AllStudy Guide

MidtermThis

**preview**shows half of the first page. to view the full**2 pages of the document.**APPM 1350 Exam 2 Spring 2017

INSTRUCTIONS: Books, notes, and electronic devices are not permitted. Write (1) your full name,

(2) 1350/Exam 2, (3) lecture number/instructor name and (4) SPRING 2017 on the front of your blue-

book. Make a grading table for 4 problems and a total. Do all problems. Start each problem on a new

page. Box your answers. A correct answer with incorrect or no supporting work may receive no credit, while

an incorrect answer with relevant work may receive partial credit. Justify your answers, show all work.

1. (a)(10pts) Find y0if y= tan(x−cos(x2)).

(b)(10pts) If xg(x)+2g0(x)=x2and g0(0) = πand g(0) = −10, ﬁnd g00(0).

(c)(5pts) Which of the ﬁve choices given below is equivalent to y0if y=sin x

x+12

? Pick only one answer,

no justiﬁcation necessary -be sure to copy down the entire answer, don’t just write down the letter of

your choice:

(A)2sin(x) cos(x)

2(x+ 1) (B)cos(x)(x+ 1) −sin(x)

(x+ 1)2(C)2sin(x) cos(x)

(x+ 1)2−2sin

2(x)

(x+ 1)3

(D)cos2(x)

(x+ 1)2(E)cos2(x)(x+ 1) −sin(x)

(x+ 1)4

2. (a)(10pts) Suppose that 3 ≤f0(x)≤5 for all values of x. Show that 18 ≤f(8) −f(2) ≤30. Hint: This

problem can be done using one of the theorems we studied. Be sure to state the theorem you are using

and justify why it applies. Show all work.

(b)(15pts) Ralphie is observing balloon launches with a telescope. Suppose a ballon is rising 400 feet

from where Ralphie is standing. If the balloon rises at a rate of 20 feet per minute, how fast is the an-

gle between the ground and the telescope changing when the balloon is 300 feet high? (See diagram below.)

Problem 2: Ralphie observes a balloon launch!

PROBLEMS #3 & #4 ON THE OTHER SIDE

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