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Midterm 2 for Calculus I for the Social Sciences - MATH 157 - D100, Exams of Calculus

Amity University - BiharCalculus

The midterm 2 for calculus i for the social sciences (math 157 - d100) held at simon fraser university in spring09. The exam consists of 5 questions and covers topics such as cost functions, derivatives, and graph analysis.

Typology: Exams

2012/2013

Uploaded on 02/18/2013

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Simon Fraser University
Department of Mathematics
Burnaby Campus
MATH 157 - D100 Spring09 Calculus I for the Social Sciences
Midterm 2 – Version 1
March 11th 2009, 11:30–12:20
Last Name (please print):
First Name (please print):
SFU Email ID: @sfu.ca
Student number:
Signature:
(do not sign before your ID is checked)
Instructor: Y. van Gennip
Instructions:
1. Do not open this booklet
until told to do so.
2. Fill in the above box. Please use
the name under which you are
registered.
3. This exam contains 7 pages with
a total of 5 questions. Once
the exam begins please check to
make sure your exam is com-
plete.
4. Show all your work! Jus-
tify your answer unless it is
specifically stated that you
do not need to.
5. If you run out of space in a prob-
lem, use the space on the back
of the previous page and clearly
indicate where the solution con-
tinues.
6. Only scientific, non-
programmable calculators with
no graphing, differentiation,
and integration capabilities are
allowed.
7. No book, paper, or device, other
than the usual writing instru-
ments, this booklet, and an
acceptable calculator shall be
within reach of a student during
the examination.
8. During the examination speak-
ing to, communicating with,
or deliberately exposing written
papers to the view of other ex-
aminees is forbidden.
9. Try your best!
Do not write in this table!
Question Marks
1/4
2/3
3/6
4/8
5/11
Total /32
1
pf3
pf4
pf5

Partial preview of the text

Download Midterm 2 for Calculus I for the Social Sciences - MATH 157 - D100 and more Exams Calculus in PDF only on Docsity!

Simon Fraser University Department of Mathematics Burnaby Campus MATH 157 - D100 Spring09 Calculus I for the Social Sciences Midterm 2 – Version 1 March 11th 2009, 11:30–12:

Last Name (please print):

First Name (please print):

SFU Email ID: @sfu.ca

Student number:

Signature: (do not sign before your ID is checked)

Instructor: Y. van Gennip

Instructions:

  1. Do not open this booklet until told to do so.
  2. Fill in the above box. Please use the name under which you are registered.
  3. This exam contains 7 pages with a total of 5 questions. Once the exam begins please check to make sure your exam is com- plete.
  4. Show all your work! Jus- tify your answer unless it is specifically stated that you do not need to.
  5. If you run out of space in a prob- lem, use the space on the back of the previous page and clearly indicate where the solution con- tinues.
  6. Only scientific, non- programmable calculators with no graphing, differentiation, and integration capabilities are allowed. 7. No book, paper, or device, other than the usual writing instru- ments, this booklet, and an acceptable calculator shall be within reach of a student during the examination. 8. During the examination speak- ing to, communicating with, or deliberately exposing written papers to the view of other ex- aminees is forbidden. 9. Try your best!

Do not write in this table! Question Marks 1 / 2 / 3 / 4 / 5 / Total /

  1. Answer the following questions with ”true” or ”false”. No explanation is necessary. [1/2 mark each = 4 marks]

(a) If the cost for producing x units is given by C(x), then C( xx ) is the marginal cost.

(b) If there is a value x = c such that f ′(c) = 0, then the graph of the function f is a horizontal line.

(c) sin(x − y) = sin x cos y − cos x sin y, for any real numbers x and y.

(d) The function f (x) = e−(x−1) 2 is increasing on the interval (−∞, 1).

(e) If the function f is continuous on the interval [a, b] and f (c) is the absolute maximum of f on this interval, then either c = a, c = b, or c is a critical number.

(f) If f (x) = g(h(x)) for some functions g and h, then f ′(x) = g′(x)h′(x).

(g) If (c, f (c)) is an inflection point for the function f , then f ′′(c) = 0 or f ′′(c) does not exist.

(h) If f is a polynomial of degree n, where n ≥ 4, then f (4)^ is a polynomial of degree at most n − 4.

  1. Compute the derivatives of the given functions. You don’t need to simplify the answer. [2 marks each = 6 marks]

(a) f (x) = tan

x^2 − 3 x+

(b) g(x) = √ (^31) x 2 −

ln(1 − x^2 )

(c) h(x) = 71xex^ + (^9899)

  1. The owner of a coffee place has computed that the average cost in dollars of making x cups of coffee during a day is given by the function C(x) =

√ 540 x+ x. He sells the coffee for $3 per cup.^ [8 marks]

(a) Compute the marginal cost function.

(b) Give a function P which expresses the profit if x cups of coffee are made and sold.

(c) Find the break-even quantity.

(d) For which number of cups of coffee sold is the profit minimal? Remember that the coffee place can only sell an integer number of cups (so no fractions or decimals as answer). What is the profit or loss in this case? Give your answer accurate up to dollar cents.

(d) Find the intervals on which f is increasing and decreasing. Find any relative extrema of f and identify them as maxima or minima.

(e) Find all intervals where f is concave up or concave down and all inflec- tion points.

(f) Use the information you have found to sketch the graph of f in the coordinate system below.