Math E-15 Homework 7
1. Consider the family of curves f (x) = xne7x where n is a positive even integer.
(a) Find the roots of f . (That is, solve f (x) = 0.)
(b) Find the x- AND y-coordinate(s) of all critical points and classify each as a local maximum,
Name:
Mathematics E-15
Exam II
April 13, 2016
Problem
1
2
3
4
5
6
7
8
9
Total
Possible
20
6
10
12
12
10
10
8
12
100
Instructions for Proctor
Please check that no student is using a TI-89 calculator, a TI-Nspire CAS calculator, or a calculator
with a QWER
Name:
Mathematics E-15
Exam I
February 24, 2016
Problem
1
2
3
4
5
6
7
8
9
Total
Possible
12
11
12
11
10
15
9
8
12
100
Instructions for Proctor
Please check that no student is using a TI-89 calculator, a TI-Nspire CAS calculator, or a calculator
with a QW
Math E-15 Homework 7a [not to be turned in]
1. A bicyclist sees an obstacle in the road 30 feet in front of her and immediately applies the brakes.
Her velocity v(t) is a decreasing function of time t where t = 0 corresponds to the moment she starts
braki
Math E-15 Homework 8
1. Compute the exact value of each of the following.
Z 1
5
(a)
dx
x
8
(b) the area under the curve y = x on the interval [1, 9]
(c) the area between the curves y = x2 8x + 24 and y = 3x
(d) the average value of f(x) = x3 on the interv
Math E-15 Homework 3a [not to be turned in]
1. For the graph of f shown, carefully sketch a graph of its derivative f 0 .
f(x)
2. The function f(x) gives the number of pounds of bananas a store sells per day as a function of the
price (in cents) per pound
Math E-15 Homework 3a [not to be turned in] - Solutions
1. For the graph of f shown, carefully sketch a graph of its derivative f 0 .
f(x)
f (x)
O
O
O
O
O
O
2. The function f(x) gives the number of pounds of bananas a store sells per day as a function
of
Math E-15 Homework 7 - Solutions
7x
1. Consider the family of curves f(x) = xn e7x
where n is a positive even integer.
(a) Find the roots of f . (That is, solve f(x) = 00.)
xn e7x = 0 xn = 0 or e7x = 0 x = 0
Note that e7x is never 0.
(b) Find the x - AND
Math E-15 Homework 9 - Solutions
1. Sketch an antiderivative F of the function f shown such that F (0) = 00. Label the x -values
a through g on your graph.
F(x)
a
b
c
d
e
f
g
e
f
g
f(x)
a
b
c
d
Please note that the antiderivative F above was drawn perfect
Math E-15 Homework 8 - Solutions
1. Compute the exact value of each of the following.
Z 1
1
5
(a)
dx = 5 ln |x| = 5 ln | 1| 5 ln | 8| = 0 5 ln 8 = 5 ln 8
x
8
8
[This is an example of why, as we discussed in class, the antiderivative of 1/x is ln |x| + C,
Math E-15 Homework 7a [not to be turned in] - Solutions
1. A bicyclist sees an obstacle in the road 30 feet in front of her and immediately applies
the brakes. Her velocity v(t) is a decreasing function of time t where t = 0 corresponds to
the moment she
Math E-15 Homework 1 - Solutions
1. y = f(x) is a linear function that gives the cost (in dollars) of using x minutes per month
on a certain cellular phone plan. If you use 100 minutes, the cost is $10; if you use 500
minutes, the cost is $18.
(a) Find a
Math E-15 Homework 2 - Solutions
1. Find all solutions x for each equation below. Give both exact answers and approximations
correct to three decimal places.
(a)
3ex = 12(72x)
ln[3ex] = ln[12(72x)]
x
Take ln of each side.
2x
ln 3 + ln(e ) = ln 12 + ln(7 )
Math E-15 Homework 4 - Solutions
1. Find the derivative of each of the following functions.
1
7
x + 7 = x7 + x1/7 + x7
x
= 7x6 + 17 x6/7 7x8
(a) y = x7 +
dy
dx
(b) y = ex xe + e77 x
dy
x
e1
(ln ) x
dx = e ex
(c) y = (x8 )(9x ) Use Product Rule.
dy
7
x
x
Math E-15 Homework 6 - Solutions
1. Find dy/dx for the curve x2 + xy + y2 = 33.
Use implicit differentiation.
x2 + xy + y2 = 3
dy
dy
2x + x
+ 1 y + 2y
= 0
dx
dx
dy
(x + 2y) = 2x y
dx
dy
2x y
=
dx
x + 2y
2. Use local linearization to estimate 33 29
29. L
Math E-15 Homework 3 - Solutions
1. Consider the function f(x) = 5x3 . Do not round off your answers to the following.
(a) What is the average rate of change of f on the interval [2, 2.1]?
f (2.1)f (2)
= 63.05
2.12
f (2.01)f (2)
= 60.3005
2.012
(b) What i
Name:
Mathematics E-15
Exam III
May 11, 2016
Problem
1
2
3
4
5
6
7
8
9
Total
Possible
16
8
12
10
10
10
14
10
10
100
Instructions for Proctor
Please check that no student is using a TI-89 calculator, a TI-Nspire CAS calculator, or a calculator
with a QWER
Name:
Mathematics E-15
Exam III
December 17, 2015
Problem
1
2
3
4
5
6
7
8
9
Total
Possible
10
8
16
12
14
10
8
12
10
100
Actual
You must show all work to receive credit.
Give exact answers (such as ln 5 or e2 ) unless requested otherwise.
Calculators wi
Math E-15 Homework 7a [not to be turned in]
1. The price that a company can charge for a particular product is a linear function of the amount of the
product available. If 1200 items are available, the price is $100 each, and if 800 items are available, t
Math E-15 Homework 8
1. Compute the exact value of each of the following.
4
x3 dx
(a)
1
/2
(b)
cos x dx
0
8
(c)
1
5
dx
x
(d) the area under the curve y =
x on the interval [1, 9]
(e) the area between the curves y = x2 8x + 24 and y = 3x
(f) the average v
Math E-15 Homework 9
1. Sketch an antiderivative F of the function f shown such that F (0) = 0. Label the x-values a through
g on your graph.
f(x)
a
b
c
d
e
f
g
2. At time t = 0 months, your company has $300 million in cash on hand. Over the next 12 month
Math E-15 Homework 6
1. Find dy/dx for the curve x2 + xy + y2 = 3.
2. Use local linearization to estimate 3 29. Leave your answer as a simplied fraction.
3. Evaluate the following limits. Simplify your answers as much as possible; for example, expressions
Math E-15 Homework 5
1. Find the derivative of each of the following functions.
(a) y = sin(7x)
(b) y = 2sin(7x)
(c) y = cos(2sin(7x)
(d) y = ln(sin(x3 )
(e) y =
arctan(log10 (5x)
3x
(f) y = e
tan(2x4 )
(g) y = sin(cos(x 23x)
(h) y = (1 + x6 )8x
(i) y =
Math E-15 Homework 2
1. Find all solutions x for each equation below. Give both exact answers and approximations correct to
three decimal places.
(a) 3ex = 12(72x)
(b) ln x = 2
(c) x3ex 6xex = 0
2. The radioactive element iodine-131 is commonly used in tr
Math E-15 Homework 3
1. Consider the function f (x) = 5x3. Do not round o your answers to the following.
(a) What is the average rate of change of f on the interval [2, 2.1]?
(b) What is the average rate of change of f on the interval [2, 2.01]?
(c) What
Math E-15 Homework 4
1. Find the derivative of each of the following functions.
1
x7
(b) y = ex xe + e7 x
(a) y = x7 +
7
x+
(c) y = (x8 )(9x )
x4 e2
3x + 17
(e) y = 53x
(d) y =
2. Consider the function f (x) = x4 4x2 .
Note: Be sure to show enough work on
Math E-15 Homework 1
1. y = f (x) is a linear function that gives the cost (in dollars) of using x minutes per month on a certain
cellular phone plan. If you use 100 minutes, the cost is $10; if you use 500 minutes, the cost is $18.
(a) Find a formula for
Name: SOQOVEEM
Mathematics E—15
Exam I
February 24, 2016
Instructions for Proctor
0 Please check that no student is using a TI—89 calculator, a TI-Nspire CAS calculator, or a calculator
with a QWERTY keyboard.
0 If any student leaves the room before com
Name, So lwk‘tom
Mathematics E—15
Exam III
May 11, 2016
Instructions for Proctor
0 Please check that no student is using a TI—89 calculator, a TI—Nspire CAS calculator, or a calculator
with a QWERTY keyboard.
0 If any student leaves the room before co