Department

MathematicsCourse Code

MATA32H3Professor

AllStudy Guide

FinalThis

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University of Toronto at Scarborough

Department of Computer and Mathematical Sciences

FINAL EXAMINATION

MATA32F - Calculus for Management I

Examiners: R. Haslhofer Date: December 13, 2015

R. Grinnell Time: 2:00 pm

E. Moore Duration: 2 hours and 50 minutes

Provide the following information

LAST NAME (CAPITALIZE)

Given Name(s) (PRINT BIG)

Student Number

Signature

Read these instructions

1. This examination has 12 numbered pages. At the beginning of the exam, check that all of

these pages are included.

2. If you need extra space for any question, use the back of a page or the blank page at the end

of the exam. Clearly indicate the location of your continuing work.

3. The following are forbidden at your work space: calculators, i-pads, smart/cell phones, all

other electronic devices (e.g. electronic translation/dictionary devices), extra paper, notes,

textbooks, opaque carrying cases, food, and drinks in paper cups/boxes or with a label.

4. You may write in pencil, pen, or other ink.

Do not write anything in the boxes below

1 2 3 4 5 6 7 8 9 10 TOTAL

16 15 16 15 14 11 16 17 14 16 150

1

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The following may be helpful

η=p/q

dp/dq S=P(1 + r)nS=R[(1 + r)n−1

r]A=R[1−(1 + r)−n

r]

n

∑

k=1

k=n(n+ 1)

2

n

∑

k=1

k2=n(n+ 1)(2n+ 1)

6

Exam Instructions Write clear neat solutions in the answer spaces provided. Full points

will be awarded only if your solutions are correct, complete, and suﬃciently display appropriate

concepts and knowledge from MATA32F.

1. (a) Let f(x) = 2(5x). Calculate f(2)(1). [3 points]

(b) Let u′(t) = 3t2−6√tand u(1) = −4. Find u(4). [5 points]

(c) Assume Newton’s method is used to approximate the number √20 and let x1= 4.

Calculate x2. [5 points]

(d) Let an eﬀective rate be reand let rbe the APR compounded quarterly that is equivalent

to re. Solve for rin terms of re. [3 points]

2

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2. The parts of this question are independent of each other.

(a) Assume yis deﬁned implicitly as a function of xby the equation 2√y+ln(xy2) = 1.

Solve for xwhen y= 1 in this equation, and then evaluate dy

dx at the point (x, 1).

[7 points]

(b) Let y=√2x(x−2)

x2+ 9 . Calculate the exact value of y′(4) and state your answer as a

fraction in lowest terms. [8 points]

3

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