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MAT137Y5 Study Guide - Quiz Guide: Qr CodeExam


Department
Mathematics
Course Code
MAT137Y5
Professor
Jaimal Thind
Study Guide
Quiz

This preview shows pages 1-3. to view the full 10 pages of the document.
University of Toronto
MAT137Y1 – Calculus!
Test 1 – 19 October 2018
Time: 110 minutes
Please complete this cover page with ALL CAPITAL LETTERS.
Last name . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
First name . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Email .................................................................@MAIL.UTORONTO.CA
Student number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
UTOR ID .......................................................................................
Instructions: (READ CAREFULLY!)
This exam booklet contains 10 pages including this one. It consists of 8 questions. The
maximum score is 41 points.
Unless otherwise noted, SHOW YOUR WORK FOR EVERY QUESTION. We may disallow
answers that have no supporting work.
If you need scratch paper, use the backs of the pages. We will only read and grade what
you write on the front of each page.
If you need extra space for a question, you may use Page 10 for this purpose. If
you do so, clearly indicate it on the corresponding problem page.
No aids of any kind are allowed or needed. In particular, no calculators and no extra scrap
paper.
Do not write or draw anything on the QR code at the top right corner of any page
Do not turn over this page until the invigilators instruct you to do so. Good luck!
1

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1. [6 points total; 2 points per part]
You do not need to justify your answers to this question.
(a) Give an example of a set Athat satisfies AZ=
Your answer: A=
(b) Give an example of a function fwith domain Rthat is continuous everywhere.
Your answer: f(x) =
(c) Give an example of a function gthat is not continuous at 0
Your answer: g(x) =
2

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2. [6 points total; 2 points per part]
Calculate the following limits (or explain that they do not exist):
(a) lim
x3
sin(3x)
xYour answer:
(b) lim
x→−∞
x2+ 2
3x2+ 4 Your answer:
(c) lim
x0
sin2(3x3)
x6Your answer:
3
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