STAT 1000 Study Guide - Midterm Guide: Memorial University Of Newfoundland
10 Nov 2016
School
Department
Course
Professor
MEMORIAL UNIVERSITY OF NEWFOUNDLAND
DEPARTMENT OF MATHEMATICS AND STATISTICS
Sample Midterm 2 MATHEMATICS 1000
Your midterm is on Thursday, March 20, 2014, 5:00-6:15 PM in ED 1020 (our usual class-
room). It will follow this format and the type of questions will be similar to those shown here.
To get the most benefit from this sample exam, I strongly advise that you review the course
material BEFORE doing these questions. Look at your assignments 5, 6, 7 and 8 to identify
areas where you had trouble. The solutions to all of these assignments will be posted to help you
understand the correct approach. Once you have reviewed, try to do these questions WITHOUT
using any notes. Solutions to the sample midterm will be posted as well.
1. Use logarithmic differentiation to find the derivatives of the following functions.
(a) y=sin3x
(5x+ 3)√x+ 4
(b) y= (x3−3x)e2x
2. (a) Find the derivative of the following function with respect to x: exy = 3x2−y
(b) Find the second derivative of the following function with respect to x:x3+y3= 5
3. Evaluate the following limits. If the limit does not exist but approaches ±∞, indicate that. You
may not use L’Hˆopital’s rule.
(a) lim
x→1
3x2−x−2
x3−1
(b) lim
x→0
cos x−cos2x
x
(c) lim
x→2x
x−2−2
x2−3x+ 2
(d) lim
x→−1
√x+ 2 −x
5x2+ 7x+ 2
4. Evaluate the following limits. If the limit does not exist but approaches ±∞, indicate that. You
may use L’Hˆopital’s rule where it applies.
(a) lim
x→∞ e−xln x(b) lim
x→0
x−x2
sin(3x)
(c) lim
x→0+xsin x
5. Find all horizontal and vertical asymptotes of f(x) = 2 + x−3x2
2x2+x−3. State their equations and
use limits to prove they are asymptotes.
6. Find and classify discontinuities of the following function. Specify the intervals where f(x) is
continuous.
f(x) =
|x+ 3|
2x−6if x≤3
cos πx
9if x > 3
7. The final question will be an extension of concept similar questions or proofs seen in class and
on assignments.
