Mid 1-09

Mid 1-09 - Ryerson University Department of Mathematics MTH...

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Unformatted text preview: Ryerson University Department of Mathematics MTH 140 Fall 2009 Test I LAST NAME: (Please print) FIRST NAME: (Please print) I.D. NUMBER: SIGNATURE: Date: October 2, 2009 Duration: 70 min. Version: White 765-BG Please indicate your section (check the appropriate box): Prof. Pascal: Prof. Wang: Prof. Bonato: Prof. Ferrando: Sec. Sec. Sec. 1 7 12 18 Sec. Sec. 2 8 Sec. Sec. 13 19 9 3 Sec. Sec. 14 20 4 Sec. Sec. 15 21 5 11 Sec. 16 22 6 10 Sec. Sec. Sec. Sec. Sec. 17 23 Sec. Sec. Sec. Sec. Sec. Sec. INSTRUCTIONS: Verify that your exam has 6 pages including this page. The use of notes, formula sheets, books or calculators is not allowed. For full-answer questions: Give full justification for your answers; correct answers alone may be worth nothing. Cross out or erase all rough work not relevant to your solution. Write your solutions in the space provided. If you need more space, use the back of the page. Indicate this fact on the original page, making sure that your solution cannot be confused with any rough work which may be there. For multiple choice questions: Make sure to write your answers in the box at the end of each question carefully. There are no part marks in the multiple-choice section and only the answer in the box will be marked. The correct response gets full marks, an incorrect response or no response gets no marks. For markers' use only: Page Value Mark 2 6 3 6 4 6 5 6 6 6 Total 30 1 MTH 140 Test I 1. (2 pts.) (multiple-choice question) following statements are true? If f (x) = log2 (x + 1) and g(x) = 3/x, then which of the Select the correct answer. A) B) C) D) There is a number c in the interval (1, 3) such that f (c) = 0. There is a number c in the interval (1, 3) such that g(c) = 0. There is a number c in the interval (1, 3) such that f (c) = g(c). None of the above are true. Write the (capital) letter of the answer in this box - - - - - - - - - - - - - 1. ------------ 2. (4 pts.) Consider the function 2 x -a x - 1 if x < 1 3 x+b if x = 1 if x > 1. ) f (x) = Are there numbers for a and b such that limx1 f (x) exists? If so, find the values of a and b and the value of the limit. Justify your answer. Answer: Option 1: The limit does not exist for any values of a and b. Check this box Option 2: a = b= limit= 2 MTH 140 Test I 3. (2 pts.) (multiple-choice question) f (x) = Find the domain of the function ln(4 - x) . 10 x Select the correct answer. A) (-, 4) C) [4, ) B) (0, 4) D) (-, 0) (0, ) E) (-, 0) [4, ) Write the (capital) letter of the answer in this box - - - - - - - - - - - - - 3. ------------ 4. (4 pts.) Find the following limit. x- ) lim x+ x2 + 2x answer: 3 MTH 140 Test I 5. (2 pts.) (multiple-choice question) terms of the tangent function. Simplify the expression sin(x + y) and express the result in cos x cos y Select the correct answer. A) tan x tan y C) 1 + tan y tan x B) tan(x + y) D) tan x tan y E) tan x + tan y Write the (capital) letter of the answer in this box - - - - - - - - - - - - - 5. ------------ ) 6. (4 pts.) Find a formula for the inverse of the function f (x) = ln(x2 - 1) - 2 ln(x + 1). answer: 4 MTH 140 Test I 7. (2 pts.)(multiple-choice question) Then lim f (x) = x Suppose that for x > 1 we have arctan 1 x 1 f (x) ln e x . Select the correct answer. A) 1 C) - 2 B) 2 D) 0 x E) The given information is insufficient for determining lim f (x) Write the (capital) letter of the answer in this box - - - - - - - - - - - - - 7. ------------ ) 8. (4 pts.) lim Find the following limit. x4 - 16 x2 x3 - 8 answer: 5 MTH 140 Test I 9. (2 pts.) (multiple-choice question) Find the limit lim 1 + |x| . 1-x x-1 Select the correct answer. A) 0 C) 1 B) -1 D) 2 E) Limit does not exist Write the (capital) letter of the answer in this box - - - - - - - - - - - - - 9. ------------ 10. (4 pts.) Find the following limit. 1 1 lim + x1 x - 1 x2 - 3x + 2 ) answer: 6 ...
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