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Math 112 Final Exam Winter 2017, Exams of Number Theory

University of Washington (UW) - TacomaNumber Theory

The final exam for Math 112 at the University of Washington in Winter 2017. It consists of 7 problems covering topics such as derivatives, marginal revenue, and water flow. The exam includes an honor statement and instructions for calculator and note usage. The typology of this document is 'exams'.

Typology: Exams

2016/2017

Uploaded on 05/11/2023

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MATH 112
Final Exam
Winter 2017
Name
Student ID # Section
HONOR STATEMENT
“I affirm that my work upholds the highest standards of honesty and academic integrity at the
University of Washington, and that I have neither given nor received any unauthorized assistance
on this exam.”
SIGNATURE:
1 16
2 18
3 12
4 12
5 16
6 12
7 14
Total 100
•Your exam should consist of this cover sheet, followed by 7 problems on 7 pages. Check that
you have a complete exam.
•You are allowed to use a TI30-XIIS calculator, a ruler, and one sheet of hand-written notes.
All other sources are forbidden.
•Do not use scratch paper. If you need more room, use the back of the page and indicate to
the grader you have done so.
•Turn your cell phone OFF and put it away for the duration of the exam.
•You may not listen to headphones or earbuds during the exam.
•Unless otherwise indicated, you must use the methods of this course and show all of your
work. Clearly label lines and points that you are using and show all calculations. The correct
answer with little or no supporting work may result in no credit. If you use a guess-and-check
method when an algebraic method is available, you may not receive full credit.
•Unless otherwise indicated, you may round your final answer to two digits after the decimal.
•There are multiple versions of the exam, you have signed an honor statement, and cheating
is a hassle for everyone involved. DO NOT CHEAT.
GOOD LUCK!
pf3
pf4
pf5
pf8

Partial preview of the text

Download Math 112 Final Exam Winter 2017 and more Exams Number Theory in PDF only on Docsity!

MATH 112

Final Exam Winter 2017

Name

Student ID # Section

HONOR STATEMENT

“I affirm that my work upholds the highest standards of honesty and academic integrity at the University of Washington, and that I have neither given nor received any unauthorized assistance on this exam.”

SIGNATURE:

Total 100

  • Your exam should consist of this cover sheet, followed by 7 problems on 7 pages. Check that you have a complete exam.
  • You are allowed to use a TI30-XIIS calculator, a ruler, and one sheet of hand-written notes. All other sources are forbidden.
  • Do not use scratch paper. If you need more room, use the back of the page and indicate to the grader you have done so.
  • Turn your cell phone OFF and put it away for the duration of the exam.
  • You may not listen to headphones or earbuds during the exam.
  • Unless otherwise indicated, you must use the methods of this course and show all of your work. Clearly label lines and points that you are using and show all calculations. The correct answer with little or no supporting work may result in no credit. If you use a guess-and-check method when an algebraic method is available, you may not receive full credit.
  • Unless otherwise indicated, you may round your final answer to two digits after the decimal.
  • There are multiple versions of the exam, you have signed an honor statement, and cheating is a hassle for everyone involved. DO NOT CHEAT.

GOOD LUCK!

  1. (16 points) Compute the indicated derivative. DO NOT SIMPLIFY.

(a) h(r, t) = te^3 r^ −

r^4

ln(t) 8

hr(r, t) =

ht(r, t) =

(b) f (x, y) = (x^2 y + xy^2 )^6

fx(x, y) =

(c) z = y^5 e(x

(^2) +4y)

∂z ∂y

  1. (12 points) The graph below shows supply and demand for a certain product.

0 1 2 3 4 5 6 7 8 9 10

10

0

1

2

3

4

5

6

7

8

9

quantity (in units)

p (in dollars per unit)

(a) On the graph above, label the demand curve, the supply curve, and the equilibrium point. (b) Use the graph to compute consumer surplus and producer surplus at equilibrium. Show all your work.

ANSWER: consumer surplus = $

ANSWER: producer surplus = $

  1. (12 points) You sell Things. The formulas below are for marginal revenue and marginal cost, where q is measured in Things and M R and M C are in dollars per Thing.

M R(q) = 540 and M C(q) = 27

√ q + 16.

Fixed Costs are $2500. Compute the maximum possible profit.

ANSWER: dollars

  1. (12 points) The graph below shows a function y = f (x).

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

20

2

4

6

8

10

12

14

16

18

f(x)

(a) Approximate the value of f ′(3).

ANSWER: f ′(3) =

(b) Approximate the value of

∫ (^6)

5

f (x) dx.

ANSWER:

∫ (^6)

5

f (x) dx =

(c) Over which of the following intervals does f ′(x) change from positive to zero to negative? Select all that apply. From x = 1 to x = 4. From x = 7 to x = 13. From x = 11 to x = 17. From x = 16 to x = 18. (d) Over which of the following intervals is f ′(x) increasing? Select all that apply. From x = 1 to x = 4. From x = 7 to x = 13. From x = 11 to x = 17. From x = 16 to x = 18.

  1. (14 points) There is a function f (x) whose formula you do not know. You know that

f (x + h) − f (x) =

2 h (2x + 2h + 3)(2x + 3)

(a) Compute f (1.05) − f (1). (Give at least three digits after the decimal in your final answer.)

ANSWER:

(b) Find the average rate of change of f (x) from x = 1 to x = 1.05. (Give at least three digits after the decimal in your final answer.)

ANSWER:

(c) Compute f ′(0.25). (Give at least three digits after the decimal in your final answer.)

ANSWER: f ′(0.25) =