Math 1600 Online
Test 2
Chapters 11 and 12
9 points each (Show all work to receive credit)
1.) Suppose that the total cost in dollars of producing x units of a product is given by
R ( x ) = 1000 xe x 50
Find the marginal revenue function.
MR = R(x)
1000 *
Math 1600
SI-Handout 6
Name:
20-points
Find the derivative and simplify. Show all work
1.) f ( x ) = 5ln x
5 x (1/x) = 5/x
2.) y = ln( x + 1)
1 x (1/x+1) = (1/x+1)
2
3.) f ( x ) = ln ( 4 x 6 x + 3)
8x 6 x (1/4x2 6x + 3)
= (8x-6)/ (4x2 6x + 3)
4.) A clothi
Math 1600
SI-Handout 5
Name:
10-points
1.) The quantity demanded per month for Bobs Jelly is related to the price per jar.
The equation:
p = 0.00042 x + 6
Where p denotes the unit price in dollars and x is the number units demanded. The
total monthly cost
Math 1600
Area Between Two Curves
Handout 8
10-points
2
2
1.) Find the area of the region enclosed by g ( x) = 1 x and f ( x) = x + x
Points of intersection
1 - x 2 = x2 + x
2x2 + x 1 = 0
(2x 1)(x + 1) = 0
x = -1
x=
Area = Right Top Bottom dx
Left
1 x2 (
MAT 1600
Project 13/14
1) S1 = 30 + 20X - .4x2 + b1 y
= 20 - .8x
20 - .8x = 0 20 = .8x x= 20/.8 x= 25
Yes, this means that sales might actually decline after some amount is spent on TV
advertising. That amount is 25 million dollars.
2) S1 = 30 + 20x - .4x
Math 1600
SI-Handout 1
Name:
10-points
Find the derivative of each. Be sure to use proper notation. Show all work.
1.) y = 5 x 8
y= -8(5)x-9
y= -40x-9
2.) f ( x) = 9 x 2 + 3 x + 4
f(x)= 2(9)x + 3
f(x) = 18x + 3
3.) f ( x) =
15 13 12
x x x +2
5
3
2
f(x) =
Math 1600
SI-Handout 4
Name:
10-points
Find the derivative of each. Be sure to use proper notation. Show all work.
1.) The weekly demand for the Pulsar 25 flat screen TV is
p = 600 0.05 x
Where p denotes the wholesale unit price in dollars and x denotes t
Math1600 Test 1
Chapters 9 and 10 Test 1
Name:
Date:
80-points total (4-points each)
1.)
Sales y ( in thousands of dollars) are related to advertising expenses x ( in
thousands of dollars) according to
y ( x) =
a.)
200 x
x + 10
Find y(2) and interpret its
Math 1600
SI-Handout 7
Name:
20-points
Integrate. Be sure to use proper notation. Show all work.
1.)
3 2 x dx
3x 2 (1/2)x2
= 3x x2 + c
2.)
2 + x + 2x
2
+ e x dx
2x + (1/2)x2 + 2 (1/3)x3 + ex + c
=2x + (1/2)x2 + (2/3)x3 + ex + c
3.)
4x
3
2
1 dx
x2
4x3
Math 1600
SI-Handout 2
Name:
10-points
Find the derivative and simplify. Show all work
x2 + 1
1.) C ( x) = 2
x 1
=2x (x2-1) (x2+1)(2x)
(x2-1)2
= 2x3-2x-2x3-2x
x4-2x2+1
= -4x_
x4-2x2+1
= -4 + 2 - 4x
x3 x
2.) y = 300 x
100 x
4x +1
= 300 100 (4x+1) 4(100x)
Math 1600
SI-Handout 3
Name:
10-points
Be sure to show all work and write sentence answers. Round to the nearest hundredth.
1.) Suppose that the cost function for a commodity is C ( x) = 400 + 7 x +
12
x
10
a.) Find the marginal cost at x = 8 and tell wha
MATH 1740
Review for Exam 2
1. Arc length and Surfaces of revolution, (Sec. 7.4)
Arc Length (#1 24, p 483)
Area of a Surface of Revolution (#39 44, p 483)
2. Work, (Sec.7.5)
Work done by a constant force, (#1 4, p 493)
Work done by a variable force (#9 34
Section 8.3
MATH 1740
Trigonometric Integrals
Integrals Involving Powers of Sine and Cosine (524)
Problem 2 (p 530) Find the indefinite integral.
Use u substitution
Problem 8* (p 530) Find the indefinite integral.
Instructor S. Babasyan
1
Instructor S. Ba
Section 8.1
MATH 1740
Basic Integration Rules
Fitting Integrands to Basic Rules
Problem 22* (p 512) Find indefinite integral.
Let
Problem 24* (p 512) Find indefinite integral.
Problem 28* (p 512) Find indefinite integral.
Problem 60 (p 512) Evaluate the d
MATH1740 CALCULUS II
Instructor S. Babasyan
Practice Test 2
Name: _ Show your work. No work, no credit.
1.
Graph the function, highlighting the part indicated by the given interval. Find the
arch length of the graph of the function over the indicated inte
Section 7.6
Moments, Centers of Mass, and Centroids
Moments and Center of Mass: One Dimensional System (487)
Let the point masses
be located at
on the x axis.
1. The moment about the origin is
2. The center of mass is
where
is the total mass of the system