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Mathematics

MATH 102

Martial Agueh

Winter

Description

UNIVERSITY OF VICTORIA
EXAMINATIONS DECEMBER 2007
MATHEMATICS 102 SECTION [F01]-[F06]
Name: Student No.:
Section:
TO BE ANSWERED ON THE PAPER Duration: 3 hours
Instructors:
[F01] Dr. M. Wyeth
[F02] Dr. M. Wyeth
[F03] Dr. E. Moore
[F04] Dr. E. McLeish
[F05] Dr. J. Ma
[F06] Dr. W. Grundlingh
STUDENTS MUST COUNT THE NUMBER OF PAGES IN THIS EXAMINATION PA-
PER BEFORE BEGINNING TO WRITE, AND REPORT ANY DISCREPANCY IMME-
DIATELY TO THE INVIGILATOR.
THIS QUESTION PAPER HAS 4 PAGES plus cover sheet and blue sheet.
Instructions:
• Fill in your name and student number in the spaces provided. Please print, and put
your family name ﬁrst.
• Sign the blue cover sheet at the back of the exam.
• The ONLY acceptable calculator is the SHARP EL-510R (B).
• No electronic devices other than your calculator are permitted.
• No paper material other than your name sheet, test paper and bubble sheet are per-
mitted.
There are 22 multiple choice questions worth 2 marks each and 8 long-answer questions
worth a total of 30 marks. The total possible mark is 74.
Section A: Multiple Choice
• On the green computer sheet print and code your family name and student number.
• Use an HB or softer pencil to enter your answers.
• For questions requiring numerical answers choose the value closest to your unrounded
answer. If your unrounded answer is equidistant from two choices, choose the larger of
the two choices.
• Do your work in the space provided. For veriﬁcation purposes show all calculations.
Unveriﬁed answers may be disallowed. If extra space is needed use the backs of the
pages.
Section B: Full answer
• For each of these questions write your answers fully and clearly on the question paper.
Marks will be deducted for incomplete or poorly presented solutions.
• If you need to use the back of a page, make sure that this is clearly marked.
At the end of the examination put your green computer sheet inside your question paper
and turn it in to the correct box for your section, version and family name initial.
Section A: ▯2=
Section B: Questions 23: 24: 25: 26:
27: 28: 29: 30:
Total: /74 Math 102 [F01]-[F06] Final Examination December 2007
Section A: Multiple Choice
2
1. Evaluate lim x ▯ 4x +4 .
x▯2 x ▯ 2
(A) ▯4 (B) ▯3 (C) ▯2 (D) ▯1 (E) 0
(F) 1 (G) 2 (H) 3 (I) 4 (J) does not exist
8x 2
2. Given f(x)= , ﬁnd lim f(x).
4x ▯ 3x ▯ 1 x▯▯
(A) ▯4 (B) ▯3 (C) ▯2 (D) ▯1 (E) 0
(F) 1 (G) 2 (H) 3 (I) 4 (J) does not exist
x ▯ 1
3. Let f(x)= . Which, if any, of the following are true statements?
x +1
(i) f(x) has a removable discontinuity at x = ▯1.
(ii) f(x) has a vertical asymptote at x = ▯1.
(iii) f(x) is continuous at x = ▯1.
(A) (i) only (B) (ii) only (C) (iii) only (D) (i) and (ii) only
(E) (i) and (iii) only (F) (ii) and (iii) only(G) all (H) none
▯
4. Given f(x) = (3x ▯ 1) 6x ▯ 2x ﬁnd f (1).
(A) 4 (B) 5 (C) 6 (D) 7 (E) 8
(F) 9 (G) 10 (H) 11 (I) 12 (J) 13
2
5. Given f(x)= 2x ▯ 3 , ﬁnd f (1).
5x +1
(A) ▯4 (B) ▯3 (C) ▯2 (D) ▯1 (E) 0
(F) 1 (G) 2 (H) 3 (I) 4 (J) does not exist
|x ▯ 4|
6. Evaluate lim ( + x).
x▯4▯ x ▯ 4
(A) ▯4 (B) ▯3 (C) -2 (D) ▯1 (E) 0
(F) 1 (G) 2 (H) 3 (I) 4 (J) does not exist
7. For the function y = x ▯1 ﬁnd ▯y and dy when x = 1 and dx =▯ x = +0.01. Which
of the following are true statements? (Numbers are rounded.)
(A) ▯y = ▯0.051 and dy = ▯0.05
(B) ▯y = ▯0.05 and dy = ▯0.051
(C) ▯y =0 .051 and dy = ▯0.05
(D) ▯y =0 .05 and dy = ▯0.051
(E) ▯y =0 .051 and dy =0 .05
(F) ▯y =0 .05 and dy =0 .051
(G) None of these
8. Suppose that the demand equation is p = 180 ▯ 0.02x and the cost function is
C(x) = 20x + 1000. Find the value of x that maximizes proﬁt.
(A) 1000 (B) 2000 (C) 3000 (D) 4000 (E) 5000
(F) 6000 (G) 7000 (H) 8000 (I) 9000 (J) 10,000
9. The straight line distance in metres traveled by an accelerating cyclist can be modeled
by s = t3/, 0 ▯ t ▯ 8 where t is the time in seconds.
2
How fast is the cyclist accelerating in m/s at t = 4?
(A) 0.1 (B) 0.2 (C) 0.3 (D) 0.4 (E) 0.5
(F) 0.6 (G) 0.7 (H) 0.8 (I) 0.9 (J) 1
Page 1 of 4 Math 102 [F01]-[F06] Final Examination (Continued) December 2007
10. Given g(x) = (x ▯ 3)2/3, ﬁnd the largest interval for which g(x) is decreasing for every
x in the interval?
(A) ▯▯ < x < 3 (B) ▯▯ < x < 0 (C) ▯▯ < x < ▯3 (D) ▯3 < x < 0
(E) ▯3 < x < 3 (F) 0 < x < 3 (G) 0 < x < ▯ (H) 3 < x < ▯
(I) ▯▯ < x < ▯ (J) none
11. A stone is dropped into a still pond creating a circular ripple. How fast in cm/s is the
2
radius increasing if the area is incre

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