MATH 137
Assignment 6
Due: 11 am, Friday, November 4
Your assignment consists of two parts.
Part 1 is available online at
http:/mapleta.uwaterloo.ca
and is due on-line by 4 pm on Thursday, November 3.
MATH 137
Tutorial #3 Problems
Wed. Sept. 24, 2014
Topic: Inverse Functions
1) For f (x) =
1
,
1 + ex
a) Find the domain and range of f (x).
Answer: D(f ) = R, R(f ) = cfw_y|0 < y < 1
1
1
1
b) Show tha
MATH 137
Tutorial #11 Problems
Wed. Nov. 26, 2014
Topic: Integration
Z
x
dt
for < x < . Find where f (x) is increasing and where
2
0 1+t+t
f (x) is concave up. Find the equation of the tangent line to
MATH 137
Tutorial #10 Problems
Wed. Nov. 19, 2014
Topics: Optimization, Newtons Method & Integration
1) Find the height of the right circular cylinder of maximum volume V which can be
placed inside a
MATH 137
Tutorial #1 Problems
Wed. Sept. 10, 2014
Topics: Inequalities and Absolute Value
1) Solve |x 3| < 2|x|. Answer: x > 1 or x < 3
2) Solve
x3 + x2
0. Answer: x > 4 or 3 < x 1 or x = 0
x2 x 12
x
MATH 137
Tutorial #5 Problems
Wed. Oct. 8, 2014
Topics: Limits, Continuity & IVT
1) Evaluate:
tan x
a) lim
x0 x + sin x
1
Answer:
2
b) lim ( x2 + 2x x2 2x)
x
Answer: 2
2) If 5 2x2 f (x) 5 x2 for 1 x 1
MATH 137
Tutorial #8 Problems
Wed. Nov. 7, 2014
Topics: Linear Approx, Differentials, Min/Max & MVT
2
1) A function f (x) has the linear approximation at a = 3 given by La (x) = 5 + (x 3).
7
Find the
Map distances Chapter 4 pg 121 127
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MATH 137
Tutorial #4 Problems
Wed. Oct. 1, 2014
Topic: Limits
1) Find a and b such that lim
x0
ax + b 2
x
!
= 1.
Answer: a = b = 4
2) Evaluate lim |x| arctan
1
.
x
x0
Answer: 0
3) If lim [f (x) + g(
MATH 137
Tutorial #6 Problems
Wed. Oct. 15, 2014
Topic: Differentiation
1) Find the equations of all lines through the point (2, 3) that are tangent to the parabola
y = x2 + x. Answer: y = 11x 25 and
MATH 137
Assignment 7
Due: Friday, November 11 by 11 am
As usual, your assignment consists of two parts.
Part 1 is available online at
http:/mapleta.uwaterloo.ca
and is due on-line by 4 pm on Thursday
MATH 137
Assignment 8
Due: Friday, November 18 by 11 am
As usual, your assignment consists of two parts.
Part 1 is available online at http:/mapleta.uwaterloo.ca,
4 pm on Thursday, November 17.
and is
MATH 137
Assignment 9
Due: Friday, November 25 by 11 am
As usual, your assignment consists of two parts.
Part 1 is available online at http:/mapleta.uwaterloo.ca.
The usual due date
is postponed by on
MATH 137
Assignment 10
Do not hand in
The following problems are recommended for you to work on. Problems such as
these may appear on the nal exam.
1. Evaluate the Riemann sum for the function y = 1 +
MATH 137
Tutorial #2 Problems
Wed. Sept. 17, 2014
Topic: Functions
1) If |x 5| < 1 use the Triangle Inequality to show that |x2 5x + 1| < 7.
2
2) Find the domain of f (x) = ln( x2 3x + 2 x). Answer: x
MATH 137
Tutorial #9 Problems
Wed. Nov. 12, 2014
Topics: Curve Sketching & lH
opitals Rule
1) Evaluate the following limits:
x sin x
1
a) lim
Answer:
x0 x tan x
2
1
1
1
b) lim
Answer:
x1 x 1
ln x
2
MATH 137
Tutorial #7 Problems
Wed. Oct. 29, 2014
Topics: Differentiation & Related Rates
1) Differentiate the following:
a) g(x) = sin |x| Does g 0 (0) exist?
x
Answer: g 0 (x) =
cos |x| (x 6= 0) , g
MATH 138
Assignment 6
Due at noon Friday March 6
Last Name :
First Name :
Student Id. #:
SECTION :
1- Determine whether sequence cfw_an converges or diverges. If it converges, nd the limit.
(a) an =