School

Ball State UniversityDepartment

Mathematical SciencesCourse Code

MATH 165Professor

AllStudy Guide

MidtermThis

**preview**shows pages 1-2. to view the full**6 pages of the document.**Math 170 - Spring 2016 - Common Final Name:

Part 1: Short Answer

•The ﬁrst six (6) pages are short answer.

•You don’t need to show work.

•Partial credit will be rare.

•When appropriate answers must include correct units.

1. (12 points) Compute each derivative. Assume that tis the input variable and:

(a) a,fand gare constants.

d

dttfg2

a=

(b) aand gare constant and fis an unknown function of t.

d

dttfg2

a=

(c) aand fare constant and gis an unknown function of t.

d

dttfg2

a=

2. (12 points) Suppose the derivative of a function is

df

dt =A√t−Be−kt

where A > 0, B > 0 and k > 0 are unknown constants. Find a possible function f.

3. (12 points) Consider the integral

Z1

0

x2+ 1

(x3+ 3x+ 1)3dx

Use the substitution u=x3+ 3x+ 1 to transform this integral into a new integral using the variable

u. Fill in the boxes below. Do not evaluate the integral.

Z

1

Only pages 1-2 are available for preview. Some parts have been intentionally blurred.

4. (16 points) The rate of change of pressure in a cylinder is given by the graph of P′(t) as shown.

Which of the following are true statements? Circle all that apply.

(a) The lowest pressure in the cylinder occurs at 6 seconds.

(b) The highest pressure in the cylinder occurs at 6 seconds.

(c) ∆P > 0 on [0,1]

(d) Z10

0

P′(t)dt < 0

(e) Z1

0

P′(t)dt < 0

(f) d2P

dt2<0 on [0,6]

(g) The pressure is decreasing between 4 and 5 seconds.

(h) P(6) > P (3).

2

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