Department

MathematicsCourse Code

MATH 2BProfessor

AllStudy Guide

MidtermThis

**preview**shows page 1. to view the full**5 pages of the document.**Fall 2014 Math 2B - First Midterm

This exam consists of 5 questions. Problems #1 and 4 are worth 15 points each, problem

#2 is worth 10 points and problems #3 and 5 are worth 25 points each. Read directions for

each problem carefully. Please show all work needed to arrive at your solutions. Clearly

indicate your ﬁnal answers.

Name :

Problem 1 : Determine whether the statement is true or false. If it is true, explain

why. If it is false, give the right result or an example that disproves the statement.

(a) If fis continuous, d

dx Zb

af(x)dx=f(x).

(b) If Z1

0f(x)dx =0, then f(x) = 0 for 0 ≤x≤1.

(c) Below is the graph of the function g. Let f(x) = Rx

0g(t)dt for all 0 ≤x≤7.

12 3 4567

−2

−1

0

1

2

3

1

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(i) fhas a local maximum at x=5.

(ii) f′(3) = 5

2.

(iii) f(2) = 0.

Problem 2 : (a) Use three rectangles and the midpoint rule to approximate the

area under the graph f(x) = 1

2x+1 and above the x-axis from x=1 to x=7.

(b) Find an expression for the same area as a limit of a Riemann sum. (You do

not need to evaluate it.)

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