Department

MathematicsCourse Code

MATH 2BProfessor

AllStudy Guide

FinalThis

**preview**shows pages 1-3. to view the full**10 pages of the document.**Math 2B: Sample Final 3

• Turn off your cell phone and do not check it during the exam.

• No calculators or other forms of assistance allowed.

• This exam consists of 12 questions for 100 total points. Points per question are in brackets.

• Read the directions for each problem carefully and answer all parts of each problem.

• Unless instructed otherwise, show all work for full credit.

• Deﬁne any notation used and label any sketches/graphs.

1. For the function drawn, estimate the area under the curve using a Riemann sum with four

subintervals and midpoints. Sketch the Riemann sum by drawing rectangles on the picture. (5)

0

1

2

3

4

5

f(x)

012345678

x

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

2

2. Evaluate the following integrals

(a) Zsin θcos2θdθ(3)

(b) Zx−7

(x+1)(x−3)dx(8)

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

3

3. Compute the average value fav of the function f(x) = xcos xon the interval [0, π

2].(7)

4. A particle has velocity v(t) = 2t−5 ft/s at time tseconds.

(a) Compute the displacement of the particle over the time inter-

val t=0 to t=3. (4)

−4

−2

0

2

v

123

t

(b) The distance travelled by the particle over the same time interval is given by

Za

05−2tdt+Z3

a2t−5dt

where ais a constant. What is the value of a?(2)

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