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Midterm

# MATH 2B Study Guide - Midterm Guide: Riemann SumExam

Department
Mathematics
Course Code
MATH 2B
Professor
All
Study Guide
Midterm

This 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

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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
x0Zx
0
sin(t)dt
x2=1
2
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