Department

MathematicsCourse Code

MATH 2BProfessor

AllStudy Guide

MidtermThis

**preview**shows pages 1-3. to view the full**10 pages of the document.**Math 2B Name (Print):

Spring 2017

Midterm 1

04/26/2017

Time Limit: 50 Minutes Student ID

This exam contains 10 pages (including this cover page) and 5 problems. Check to see if any pages

are missing. Enter all requested information on the top of this page, and put your initials on the

top of every page, in case the pages become separated.

You may not use your books, notes, or any calculator on this exam.

You are required to show your work on each problem on this exam. The following rules apply:

•If you use a “theorem” you must indicate

this and explain why the theorem may be applied.

•Organize your work, in a reasonably neat and

coherent way, in the space provided. Work scat-

tered all over the page without a clear ordering

will receive very little credit.

•Mysterious or unsupported answers will not

receive full credit. A correct answer, unsup-

ported by calculations, explanation, or algebraic

work will receive no credit; an incorrect answer

supported by substantially correct calculations and

explanations might still receive partial credit.

•If you need more space, use the back of the pages;

clearly indicate when you have done this.

Do not write in the table to the right.

Problem Points Score

1 15

2 12

3 20

4 18

5 14

Total: 79

Only pages 1-3 are available for preview. Some parts have been intentionally blurred.

Math 2B Midterm 1 - Page 2 of 10 04/26/2017

1. Determine if the following statements are true or false. For each case explain your answers.

(a) (3 points) The function deﬁned by

f(x) = sin(x)

xif x6= 0

1 if x= 0

is integrable in the interval [−1,1]

(b) (3 points)

Z1

−1x5+ cos(x) sin(x)dx = 0

(c) (3 points)

Zπ/4

0

(x+ 1)2cos2(x)dx = 0

Only pages 1-3 are available for preview. Some parts have been intentionally blurred.

Math 2B Midterm 1 - Page 3 of 10 04/26/2017

(d) (3 points) If a continuous function fsatisﬁes

Z1

0

f(x)dx = 0

then f(x) = 0 for x∈[0,1].

(e) (3 points)

lim

x→0Zx

0

sin(t)dt

x2=1

2

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