





Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
A midterm exam for the math 150 course at simon fraser university, taught by dr. Mulholland in the fall 2006 semester. The exam covers various topics in mathematics, including limits, continuity, and functions. Students are required to answer questions related to computing limits, identifying even functions, and applying the squeeze law. The exam consists of five questions, each worth a different number of points, totaling 40 points.
Typology: Exams
1 / 9
This page cannot be seen from the preview
Don't miss anything!






MATH 150 Fall 2006 Instructor: Dr. Mulholland October 4, 2006, 8:30 โ 9:20 a.m.
Name: (please print) family name given name
student number SFU-email
Signature:
Instructions:
Question Maximum Score
[3] (a) lim xโโ 1 (x^3 โ 2 x^2 + 5x + 1)^2
[3] (b) lim xโ 5
x โ 1 โ 2 x โ 5
give an example for which the statement doesnโt hold).
[2] (a) If f is one-to-one, then f โ^1 (x) =
f (x)
[2] (b) The function g(x) = x sin (x) is an even function.
[2] (c) Suppose that a continuous function f (x) satisfies the following table of values.
x โ 1 โ 0. 5 0 0. 5 1 1. 5 2 2. 5 3 f (x) โ 3 โ 1. 25 0. 25 0. 75 1 0. 75 โ 0. 25 โ 1. 25 โ 3
Then the function f (x) has at least 2 zeros in the interval (โ 1 , 3).
[2] (d) If f has domain [0, โ) and has no horizontal asymptote, then limxโโ f (x) = โ or limxโโ f (x) = โโ.
[3] (b) Suppose that
g(x) =
x^2 โ 1 if x โค 0 , bx^3 โ 2 if 0 < x โค 1 , 2 x โ b if x > 1 , where b is some constant.
Is the function g continuous at x = 0? Justify your answer.
[4] (b) Use the Squeeze Law to compute lim xโ 0 +
xesin (ฯ/x). Justify your answer.
lim hโ 0
f (2 + h) โ f (2) h where f (x) = x^3 โ 1.