MATH 155 Midterm 1 Exam at Simon Fraser University, Exams of Calculus

A past exam from math 155 at simon fraser university, held on 7 february 2007. It includes instructions for the exam and six math problems covering topics such as calculus, definite integrals, and volumes of solids of revolution.

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SIMON FRASER UNIVERSITY
MATH 155 Midterm 1
7 February 2007, 08:30–09:20
Last Name
Given Name(s)
Student #
Signature
INSTRUCTIONS
1. Do not open this booklet until told to do so.
2. Write your last name, given name(s), and student num-
ber in the box above. Sign on the last line of the box.
3. This exam has 6 questions on 5 pages. Check to make
sure that your exam is complete.
4. No book, paper or device other than usual writing in-
struments, this examination booklet, and a scientific
calculator are allowed. Calculators with graphing
and/or symbolic computation capabilities are not
allowed.
5. During the examination, speaking to, communi-
cating with, or exposing written papers to the
view of other examinees is forbidden.
6. You may use the reverse side of the previous page
for rough work or if you run out of space.
7. You may lose marks if your explanations are in-
complete or poorly presented.
8. Stop writing when you are instructed to do so.
Failure to follow instructions may result in penal-
ties.
Question Maximum Score
17
2 8
35
4 5
56
6 8
Total 39
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pf4
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Partial preview of the text

Download MATH 155 Midterm 1 Exam at Simon Fraser University and more Exams Calculus in PDF only on Docsity!

SIMON FRASER UNIVERSITY

MATH 155 Midterm 1

7 February 2007, 08:30–09:

Last Name

Given Name(s)

Student #

Signature

INSTRUCTIONS

  1. Do not open this booklet until told to do so.
  2. Write your last name, given name(s), and student num- ber in the box above. Sign on the last line of the box.
  3. This exam has 6 questions on 5 pages. Check to make sure that your exam is complete.
  4. No book, paper or device other than usual writing in- struments, this examination booklet, and a scientific calculator are allowed. Calculators with graphing and/or symbolic computation capabilities are not allowed.
  5. During the examination, speaking to, communi- cating with, or exposing written papers to the view of other examinees is forbidden.
  6. You may use the reverse side of the previous page for rough work or if you run out of space.
  7. You may lose marks if your explanations are in- complete or poorly presented.
  8. Stop writing when you are instructed to do so. Failure to follow instructions may result in penal- ties.

Question Maximum Score 1 7

2 8

3 5

4 5

5 6

6 8

Total 39

  1. Clearly indicate if the following statements are true (T) or false (F).

Assume that all functions are continuous in the intervals of inte- gration.

A statement containing general constants and/or functions (f, g, a, b, c, n) is true if and only if it holds for all admissible choices of these constants and/or functions.

[1] (a)

∑n k=1(k^ + 1) =^

n(n + 3) 2

[1] (b)

∫ (^) b a f^ (x)g(x)^ dx^ =

(∫ (^) b a f^ (x)^ dx

(∫ (^) b a g(x)^ dx

[1] (c) If

∫ (^) b a f^ (x)^ dx^ ≥^0 , then^ f^ (x)^ ≥^0 for all^ x^ in^ [a, b].

[1] (d) If f (x) ≥ c for all x in [a, b], then

∫ (^) b a f^ (x)^ dx^ ≥^ c.

[1] (e)

0 x^ sin^ x dx^ ≤^

[1] (f)

∫ (^) b a [f^ (x)^ −^ g(x)]^ dx^ =

(∫ (^) b a f^ (x)^ dx

(∫ (^) b a g(x)^ dx

[1] (g)

∫ (^) b a f^ (x)^ dx^ =^

(∫ (^) c a f^ (x)^ dx

(∫ (^) c b f^ (x)^ dx

[5] 3. Determine the average value of f (x) =

1 − x^2

in the interval [0, 1 /2].

[5] 4. Express the area between the curves y = 2x^2 + 4 and y = 7 − x^2 as a definite integral. DO NOT EVALUATE THE INTEGRAL.

[3] 5. (a) Describe the right-circular cone with base radius r and height h as a solid of revolution.

[3] (b) Use the formula for the volume of a solid of revolution to express the volume of the right-circular cone with base radius r and height h as a definite integral. DO NOT EVALUATE THE INTEGRAL.