MTH 132 Quiz 1 SOLUTIONS
Sections 7.2 and 7.3 (9/16)
Show all necessary work for full credit. Partial credit will be awarded for
1.[10 points] Find the value of the following improper integral by taking a
limit. If the limit diverges
Use the gaph of the relative rate of growth of a population with f in years to determine the
percentage change in population over 12 years. Be sure to indicate whether increase or decrease.
Use the density fi:nction p(t),shown below, to draw the graph of the associated cr:mulative
distribution finction. Note: you must determine &e value of a. In addition, you must put a
scale on the vertical axis for P.
2 October 2014
Problems 1 - 6 are worth 10 points each. Problem 7 and the Bonus are worth 10 each.
1) Find the antiderivative of f (x)
(2x + 1)3.
(.f . Zx vl
lr-1 - L'd
2) Find an antiderivative
MTH 132 Practice Exam II
Due Monday, Nov. 22
1. For each the following functions, draw the cross-sections of the function
with x xed, x = 0, 1, 2, and for y xed, y = 0, 1, 2
(a) f (x, y ) = 2x + y
(b) g (x, y ) = x2 + y 2 + 6x + 9
(c) h(x, y ) = 2x2 2y
Integration by Parts Homework
Due Wednesday, 9/23
Find the antiderivatives using integration by parts.
v du = uv
Let f (x) = x, df = 1dx, dg = ex dx, and g (x) = ex . Then
xex dx = xex
ex dx = xex ex + C
(x3 + 3x2 )ln(x)dx
MTH 132 Quiz 4 SOLUTIONS
1. [10 points] A manufacturer Hard Hats produces football helmets and motorcycle helmets. If football helmets sell for $75 and motorcycle helmets sell for
$150, determine the manufacturers revenue R as a function
Interpreting multiple variables
If we consider the concentration s of a drug in the blood stream t hours after
a dosage of x mg as a function of both x and t, we can get basic information
about s by looking at the cross-sections.
MTH 132 Practice Exam I
Show all neccessary work for full credit. You may work on a separate piece of
paper if you prefer, but make sure to submit all additional pages.
Evaluate each improper integral. If the integral does not exist, write does n
MTH 132 Quiz 2
1.[10 points] Find a value for the constant k so that the function
p(x) = kx 0 x 4
is a probability density.
In order for p(x) to be a density, it must be non-negative and it must integrate
to 1. It will b
F( b; -
| \2. t 9+L
;r*^ *roJ u^", A'l\4"leat,
a<_dxts \arqcjrncF k,
1) Using the grap! of F'(r)
and the fact that
F(0) = 2, complete the table for values of F.
I F'i+r i