M134-Test1-F09

# M134-Test1-F09 - x → cos(3 x sin(5 x cos(2 x sin(6 x[3(c...

This preview shows pages 1–6. Sign up to view the full content.

MCS @UTM MAT 134Y5Y Term Test 1 Friday, Oct 9, 2009 Last Name: Given Name: Student #: Tues 11 12 1 5 6 7 Thurs 11 12 1 5 6 7 Please Circle Your Tutorial. Allowed Aids: Non-graphing Calculator Duration: 110 minutes. Answer all questions. Show your work. There are 6 pages including this cover page but not including the signature page. Qn# Value Score 1 10 2 10 3 10 4 10 5 10 Total 50 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
1. (a) Solve | 3 x - 1 | < 1 . Show your answer in interval notation. [4] (b) Find f - 1 when y = f ( x ) = ln( e x + 1) . [4] (c) Let f ( x ) = x 2 - 4 , g ( x ) = x + 4 . Find formulas for f g and g f . [2] 2
2. (a) Sketch the graph of y = sin(2 πx - π ) , 0 x 1 . [4] (b) Sketch the graph of y = sin - 1 ( x ) . [2] (c) Find the value of sin - 1 ( tan ( 15 π 4 )) . [2] (d) What are the values of x ± - π 2 , π 2 ² that belong to the domain of y = sin - 1 (tan x ) ? [2] 3

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
3. Evaluate the following limits. (a) lim x →- 3 x 2 + x - 6 x 2 + 4 x + 3 [4] (b) lim

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: x → cos(3 x ) sin(5 x ) cos(2 x ) sin(6 x ) [3] (c) lim x → + ∞ 6 x + 1 √ x 2-1 + x [3] 4 4. Let f ( x ) = 3 x 2 + 1 x-1 . (a) Find all horizontal, vertical, and oblique asymptotes of f . [6] (b) Guess the graph of f and draw a rough sketch. [2] (c) Does f have an inverse? State ( brieﬂy ) a reason for your answer. [2] 5 5. Let f ( x ) = 4 e 1 /x + 6 6 e 1 /x + 9 . (a) Find lim x →-e 1 /x . [2] (b) Find lim x → + e 1 /x . [2] (c) Which of the following statements is true? Justify your answer. [6] (i) f has a vertical asymptote at x = 0 . (ii) f has a jump discontinuity at x = 0 . (iii) f has a continuous extension to x = 0 . 6...
View Full Document

## This note was uploaded on 01/30/2011 for the course BIO 200 taught by Professor B during the Fall '10 term at University of Toronto.

### Page1 / 6

M134-Test1-F09 - x → cos(3 x sin(5 x cos(2 x sin(6 x[3(c...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online