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Stewart -Essential Calculus 1/e (Homework)

James Finch

Math - College, section 1, Fall 2010

Instructor: Dr. Friendly

Current Score: 13/43

Due: Tuesday, October 5, 2010 22:00 EDT

About this Assignment

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Question
Points
1 2 3 4 5 6 7 8
12 0/10 0/1 0/2 0/4 0/1 0/1 1/12
Total
13/43

Description

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Now Stewart's proven problem-solving approach becomes the foundation of Enhanced WebAssign for Stewart's Essential Calculus. You will be able to choose from over 5000 textbook problems to assign in WebAssign's secure online environment, each one with a detailed solution available to students at your discretion.


And, to help students master critical calculus concepts Enhanced WebAssign includes enhanced content, specifically linking homework problems to interactive tools, tutorials and examples authored by Jim Stewart.


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You can check out a sampling of this exciting development below.


Questions 1, 4, and 6 are traditional, free response end-of-section/chapter questions, with detailed algorithmic solution. (For this demo, the solution can be displayed immediately after the question has been submitted rather than the normal way of after the assignment is past due.)


Question 2 is an Active Example which helps guide students through the process needed to master a concept. Included are links to the specific section of the online textbook, video solution, and stepwise tutorial question.


Question 3 is a Stepwise Tutorial Question that helps show students how to solve the problem. Please note that students are provided an option to answer the question without having to work through all the steps.


Question 5 is a question involving an algorithmically generated graph.


Question 7 is a free response with math palette for entering the answer. (For this demo, the solution can be displayed immediately after the question has been submitted rather than the normal way of after the assignment is past due.)


Question 8 is a representative selection of problems from Stewart's new Diagnostic Tests. The Diagnostic Tests allow students to review their existing math skills before starting the calculus sequence, covering algebra, analytic geometry, trigonometry, and functions. For students that need additional help, James Stewart has written review content that can be accessed just-in-time while working through the diagnostic problems. This example problem represents just a few of the algebra questions.


Instructions

This demo assignment allows many submissions and allows you to try another version of the same question for practice.



1. 12/12 points All Submissions Notes Question: SEssCalc1 1.1.001.
Question part
Points
Submissions
1 2 3 4 5 6 7 8 9 10 11 12
1 1 1 1 1 1 1 1 1 1 1 1
2/50 1/50 2/50 1/50 4/50 1/50 2/50 1/50 1/50 1/50 2/50 1/50
Total
12/12
 
The graph of a function f is given.
(a) State the value of f(-1).
Enter a number.
Your answer is correct.

(b) Estimate the value of f(2).
Enter a number.
Your answer is correct.

(c) For what values of x is f(x) = 2?
Enter a number.
Your answer is correct. (smaller value)
Enter a number.
Your answer is correct. (larger value)

(d) Estimate the values of x such that f(x) = 0.
Enter a number.
Your answer is correct. (smaller value)
Enter a number.
Your answer is correct. (larger value)

(e) State the domain and range of f.
[
Enter a number.
Your answer is correct.
Enter a number.
Your answer is correct.]		domain
[
Enter a number.
Your answer is correct.
Enter a number.
Your answer is correct.]		range

(f) On what interval is f increasing?
(
Enter a number.
Your answer is correct.,
Enter a number.
Your answer is correct.)


2. –/10 points Notes Question: SEssCalc1 2.1.AE.01.
Question part
Points
Submissions
1 2 3 4 5 6 7 8 9 10
0/1 0/1 0/1 0/1 0/1 0/1 0/1 0/1 0/1 0/1
0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50
Total
0/10
 
Maple Generated Plot
Video Example
Tutorial
Online Textbook

EXAMPLE 1 Find an equation of the tangent line to the function y = 3x4 at the point P(1, 3).

SOLUTION We will be able to find an equation of the tangent line t as soon as we know its slope m. The difficulty is that we know only one point, P, on t, whereas we need two points to compute the slope. But observe that we can compute an approximation to m by choosing a nearby point Q(x, 3x4) on the graph and computing the slope mPQ of the secant line PQ. We choose x 1 so that P Q. Then

mPQ = 3x4 - 3

x - 1

For instance, for the point Q(1.5, 15.1875) we have

mPQ =
Enter a number.
 - 3

Enter a number.
 - 1		 =
Enter a number.


.5		 =
Enter a number.

The tables below show the values of mPQ for several values of x close to 1. The closer Q is to P, the closer x is to 1 and, it appears from the tables, the closer mPQ is to

Enter a number.
. This suggests that the slope of the tangent line t should be m =
Enter a number.
.

xmPQxmPQ
24503
1.524.3750.55.625
1.113.9230.910.317
1.0112.1810.9911.821
1.00112.0180.99911.982

We say that the slope of the tangent line is the limit of the slopes of secant lines, and we express this symbolically by writing

lim_(Q->P) m_(PQ) = 12     text(and)     lim_(x->1) (3 x^4 - 3)/(x-1) = 12

Assuming that the slope of the tangent line is indeed 12, we use the point-slope form of the equation of a line (see Appendix B) to write the equation of the tangent line through (1, 3) as

y -
Enter a number.
 =
Enter a number.
(x - 1) or y =
Enter a number.
x -
Enter a number.

The graphs below illustrate the limiting process that occurs in this example. As Q approaches P along the graph, the corresponding secant lines rotate about P and approach the tangent line t.



3. –/1 points Notes Question: SEssCalc1 2.6.Tut.01.
Question part
Points
Submissions
1
0/1
0/50
Total
0/1
 



4. –/2 points Notes Question: SEssCalc1 3.1.025.
Question part
Points
Submissions
1 2
0/1 0/1
0/50 0/50
Total
0/2
 
Find the critical numbers of the function.
f(x) = x3 + 3x2 - 24x
x =
Enter an exact number.
 (smaller value)
x =
Enter an exact number.
 (larger value)

5. –/4 points Notes Question: SEssCalc1 4.1.001.
Question part
Points
Submissions
1 2 3 4
0/1 0/1 0/1 0/1
0/50 0/50 0/50 0/50
Total
0/4
 
Do the following.
a = 50
(a) By reading values from the given graph of f, use five rectangles to find a lower estimate and an upper estimate for the area under the given graph of f from x = 0 to x = 100.

A
Enter a number.
 (lower estimate)
A
Enter a number.
 (upper estimate)

(b) Find new estimates using ten rectangles in each case.

A
Enter a number.
 (lower estimate)
A
Enter a number.
 (upper estimate)


6. –/1 points Notes Question: SEssCalc1 7.1.004.
Question part
Points
Submissions
1
0/1
0/50
Total
0/1
 
Consider the following shaded region.
Find the area S of the shaded region if a = 3, b = 1.
S =
Enter an exact number as an integer, fraction, or decimal.


7. –/1 points Notes Question: SEssCalc1 6.1.003.
Question part
Points
Submissions
1
0/1
0/50
Total
0/1
 
Evaluate the integral.
int 3 x cos 5 x text( )dx
+ C

8. 1/12 points All Submissions Notes Question: SEssCalc1 Diagnostic.Algebra.demo
Question part
Points
Submissions
1 2 3 4 5 6 7 8 9 10 11 12
1 0/1 0/1 0/1 0/1 0/1 0/1 0/1 0/1 0/1 0/1 0/1
1/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50
Total
1/12
 
4) Factor each expression.
(a) 4x2 - 25 = <math><mrow><mfenced close=")" open="("><mn>2</mn><mi>x</mi><mo>+</mo><mn>5</mn></mfenced><mfenced close=")" open="("><mn>2</mn><mi>x</mi><mo>-</mo><mn>5</mn></mfenced></mrow></math> Your answer is correct.

(b) 2x2 + 5x - 12 =

(c) x3 - 3x2 - 4x + 12 =

(d) x4 + 27x =

(e) 3x3/2 - 9x1/2 + 6x-1/2 =

(f) x3y - 4xy =


9) Solve each inequality. Write your answer using interval notation. (If you need to use - or , enter -INFINITY or INFINITY.)
(a) -4<5-3x<=17
Answer is not case sensitive.


(b) x^2<2x+8
Answer is not case sensitive.


(c) x(x-1)(x+2) > 0
Answer is not case sensitive.
Answer is not case sensitive.


(d) abs(x-4)<3
Answer is not case sensitive.


(e) (2x-3)/(x+1)<=1
Answer is not case sensitive.


If you have had difficulty with these problems, you may wish to consult the Review of Algebra on the website StewartCalculus.com.

NOTE FROM WEBASSIGN: This question is just a representative sample of available problems from Stewart's new Diagnostic Tests, which allow students to review their existing math skills in algebra, analytic geometry, trigonometry and functions. A complete Diagnostic Test for each of these subject areas (along with review material written by James Stewart) is available to help your students get up to speed.
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