Differential Calculus with Applications to Commerce and Social Sciences
MATH 104

Summer 2015
Written Homework 2 MATH 104921
Henrik Rping
u
due Tuesday, May 26th 2015
Exercise 1: [9] Let us have a look at the function
f (x) =
x2 sin(1/x)
0
if x = 0
.
if x = 0
You may use that the derivative of sin(x) is cos(x).
1. What is f (a) for a = 0?
2. What
Differential Calculus with Applications to Commerce and Social Sciences
MATH 104

Summer 2015
Things you should know for the nal
Henrik Rping
u
June 2015
1. Domain and Range of functions
2. Limits
(a) Denition of Limits
(b) Limits from the left and the right
(c) Limits at innity (limx ) and innite limits limxa f (x) = .
(d) How to compute Limits
(
Differential Calculus with Applications to Commerce and Social Sciences
MATH 104

Fall 2012
Frances Chong
Assignment Assignment3 due 10/01/2014 at 08:00am PDT
MATH104184ALL 2014W1
1. (1 pt) Match the blue graph of each function to the black
graph of its derivative by writing the letter (A, B, C, or D) of the
blue graph next to the appropriate
Differential Calculus with Applications to Commerce and Social Sciences
MATH 104

Fall 2012
Frances Chong
Assignment Assignment10 due 11/24/2014 at 08:00am PST
1. (1 pt) Find the linearization L(x) of the function f (x) =
x4 + 3x2 2 at x = 2.
Answer: L(x) =
Use linear approximation to estimate f (2.1):
Is your answer a little too big or a little
Differential Calculus with Applications to Commerce and Social Sciences
MATH 104

Fall 2012
Frances Chong
Assignment Assignment2 due 09/24/2014 at 08:00am PDT
1. (1 pt)
If f and g are continuous functions with f (0) = 3 and
lim f (x)g(x) = 6, find g(0).
MATH104184ALL 2014W1
7. (1 pt)
From the graph of g, state whether or not g is continuous
(e
Differential Calculus with Applications to Commerce and Social Sciences
MATH 104

Fall 2012
Frances Chong
Assignment Assignment1 due 09/17/2014 at 08:00am PDT
MATH104184ALL 2014W1
8. (1 pt)
Evaluate the limit, by using the appropriate Limit Law(s).
3
1 + 3x
lim
x1 1 + 4x2 + 3x4
1. (1 pt)
Evaluate the limit, by using the appropriate Limit Law(s
Differential Calculus with Applications to Commerce and Social Sciences
MATH 104

Fall 2012
Frances Chong
Assignment Assignment6 due 10/22/2014 at 08:00am PDT
MATH104184ALL 2014W1
(a) One is a reflection over the xaxis of the other.
(b) One is a reflection over the yaxis of the other.
(c) Both (a) and (b).
(d) None of the above.
1. (1 pt)
Wh
Differential Calculus with Applications to Commerce and Social Sciences
MATH 104

Fall 2012
Frances Chong
Assignment Assignment7 due 10/29/2014 at 08:00am PDT
1. (1 pt) At noon, ship A is 150km west of ship B. Ship A
is sailing south at 45km/h and ship B is sailing north at 25km/h.
How fast is the distance between the ships changing at 4:00pm.
A
Differential Calculus with Applications to Commerce and Social Sciences
MATH 104

Fall 2012
Frances Chong
Assignment Assignment9 due 11/16/2014 at 08:00am PST
MATH104184ALL 2014W1
8. (1 pt) A carpenter has been asked to build an open box
with a square base, where an open box means a box without a
top. The sides of the box will cost $3 per squa
Differential Calculus with Applications to Commerce and Social Sciences
MATH 104

Fall 2011
MATH104/184
Business Optimization Problems
MATH 104/184
November 17, 2011
1. A fuel tank of volume 144 cubic meters consists of a cylindrical part
capped by hemispheres at each end. The construction cost is $5 per
square meter for the cylindrical wall, bu
Differential Calculus with Applications to Commerce and Social Sciences
MATH 104

Fall 2011
Price Elasticity of Demand
MATH 104
Mark Mac Lean (with assistance from Patrick Chan)
2011W
The price elasticity of demand (which is often shortened to demand
elasticity) is dened to be the percentage change in quantity demanded, q ,
divided by the percen
Differential Calculus with Applications to Commerce and Social Sciences
MATH 104

Fall 2011
Related Rates Problems Solutions
MATH 104/184
2011W
1. The workers in a union are concerned whether they are getting paid
fairly or not. They are specically concerned at the rate at which
wages are increasing per year is lagging behind the rate of increas
Differential Calculus with Applications to Commerce and Social Sciences
MATH 104

Fall 2011
Extra Problems #1
MATH 104 and Math 184
September 26, 2011
1. Consider the cost function C (q ) = 6q 2 + 14q + 18 (in thousands of dollars).
(a) What is the marginal cost at production level q = 5?
(b) Estimate the cost of raising the production level fro
Differential Calculus with Applications to Commerce and Social Sciences
MATH 104

Fall 2011
9, Lu T1 o'PJ
Narrtp:
SrunpNr NuMenR:
Assignment ff L
MATH L04 Section 103
Due: Friday, October 7, 20LI
Question 1: Consider the function
f(r\:["'*rifrll
'\ /
[ar+bif r>L
(a) Find a/ values of the constants n and b that make /(r) a continuous
function at
Differential Calculus with Applications to Commerce and Social Sciences
MATH 104

Fall 2011
MATH 104
QL
Mocx MrornRru 2
3L October

201"1
 p.2 of.7
[10 marks]
p.m. ship A is 25 km due north of ship B. If ship A is sailing west at a rate of 16 km/h
and ship B is sailing south at 20 km/h, find the rate at which the distance between the two
ship
Differential Calculus with Applications to Commerce and Social Sciences
MATH 104

Fall 2011
PROBLEM SET 3
1. Tiany sleeps 8 hours per day. She has a summer job that allows her to work any
number of hours per day (up to 8 hours) at $6 per hour. The remaining hours are
spent doing mathematics. Her mother gives her an allowance of $6 per day.
The a
Differential Calculus with Applications to Commerce and Social Sciences
MATH 104

Fall 2011
PROBLEM SET 2
Tiany sleeps 8 hours per day. She has a summer job that allows her to work any number
of hours per day (up to 8 hours) at $6 per hour. The remaining hours are spent doing
mathematics. Her mother gives her an allowance of $6 per day.
The amou