Department

MathematicsCourse Code

MAT137Y5Professor

Jaimal ThindStudy Guide

QuizThis

**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.

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Email .................................................................@MAIL.UTORONTO.CA

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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 A∩Z=∅

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

x→3

sin(3x)

xYour answer:

(b) lim

x→−∞

x2+ 2

3x2+ 4 Your answer:

(c) lim

x→0

sin2(3x3)

x6Your answer:

3

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