MATH113 Midterm: MATH113 Midterm 2011 Winter
MATHEMATICS 113 (S1)
Midterm Examination, Version 1
Winter 2011
Date: Wednesday, March 09, 2011
Instructor: E. Osmanagic Time: 50 minutes
LAST NAME: FIRST NAME:
(Please, print!)
Instructions
1. Books, notes or calculators are not permitted.
2. Show all your work.
3. Make sure your examination paper has 5 questions.
ID#: Name:
Instructions
1. Books, notes or calculators are not permitted.
2. Show all your work.
3. Make sure your examination paper has 5 questions.
Question Value Your Mark
120
210
310
410
510
Total 60
Document Summary
Instructions: books, notes or calculators are not permitted, show all your work, make sure your examination paper has 5 questions. Name: (20 points) (a) find the domain of f if f (x) = Df = {x r |8 x2 2x 0} = {x r |x2+2x 8 0} = {x r |(x+4)(x 2) 0} = [ 4, 2] (b) find horizontal and vertical asymptotes of f (x) = 2 3x2 x2+2x 3. = 3, lim x x2 + 2x 3 y = 3 is a horizontal asymptote. Since x2 + 2x 3 = 0 for x = 3 or x = 1, candidates for vertical asymptotes are x = 3 and x = 1. x2 + 2x 3 x lim lim x 3 . 2 3x2 x2 + 2x 3. 2 3x2 x2 + 2x 3 lim x 1+ Hence, x = 3 and x = 1 are vertical asymptotes. x2 + 2x 3 lim x 1 (c) evaluate.
