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Rogawski - Calculus (Homework)

James Finch

Math - College, section 1, Fall 2010

Instructor: Dr. Friendly

Current Score: 3/13

Due: Tuesday, September 14, 2010 22:00 EDT

About this Assignment

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Question
Points
1 2 3 4 5 6 7
1 0/2 2 0/2 0/1 0/1 0/4
Total
3/13

Description

W. H. Freeman and WebAssign

W. H. Freeman and WebAssign have partnered to deliver an outstanding resource for your calculus course.

Combining the mostly widely used online homework platform and a new textbook that presents calculus with a solid mathematical precision but with everyday sensibility that puts the main concepts in clear terms, Ragowski's Calculus is rigorous without being inaccessible and clear without being too informal-it has the perfect balance for instructors and their students.

The WebAssign homework and assessment system will provide instructors with 1200 new problems, virtually all of which are randomized. This system is available both with a print or an eBook version of the text.

Click here to learn more about our careful, precise development, the distinct features of this text or to see a sample chapter.

Here are some textbook questions from Calculus 1/e by Jon Rogawski published by W. H. Freeman. Click here for a list of all of the questions coded in WebAssign.


Instructions

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



1. 1/1 points All Submissions Notes Question: RogaCalc1 3.3.016.
Question part
Points
Submissions
1
1
1/50
Total
1/1
 
Consider the function.
z =
x
x4 + 3
Find the value of the derivative at the given point.
dz
dx


x = -3		 =
Enter a mathematical expression or equation with exact values.
Your answer is correct.


2. –/2 points Notes Question: RogaCalc1 3.3.038.
Question part
Points
Submissions
1 2
0/1 0/1
0/50 0/50
Total
0/2
 
Consider the curve defined below.
Maple Generated Plot
y =
1
x 2 + 1
This curve is called the witch of Agnesi after the Italian mathematician Maria Agnesi (1718-1799) who wrote one of the first books on calculus. This strange name is the result of a mistranslation of the Italian word la versiera, meaning "that which turns." Find equations of the tangent lines at x = ±3
Enter a mathematical expression or equation with exact values.
Click here to preview your answer. (x = 3)

Enter a mathematical expression or equation with exact values.
Click here to preview your answer. (x = -3)


3. 2/2 points All Submissions Notes Question: RogaCalc1 3.4.020.
Question part
Points
Submissions
1 2
1 1
1/50 1/50
Total
2/2
 
The position of a particle moving in a straight line during a 3-s trip is given below.
s(t) = 3t 2 - 8t + 5 cm
(a) What is the average velocity for the entire trip? (Assume the 3 second interval starts at t = 0.)
Enter a mathematical expression or equation with exact values.
Your answer is correct. cm/s

(b) Find a time at which the instantaneous velocity is equal to this average velocity.
Enter a mathematical expression or equation with exact values.
Your answer is correct. s

4. –/2 points Notes Question: RogaCalc1 3.5.008.
Question part
Points
Submissions
1 2
0/1 0/1
0/50 0/50
Total
0/2
 
Consider the function defined below.
y = x-3/2
Calculate the second and third derivatives.
y '' =
Enter a mathematical expression or equation with exact values.
Click here to preview your answer.
y ''' =
Enter a mathematical expression or equation with exact values.
Click here to preview your answer.

5. –/1 points Notes Question: RogaCalc1 3.6.042.
Question part
Points
Submissions
1
0/1
0/50
Total
0/1
 
Consider the function.
y = sin(x)
y(108) =
Enter a mathematical expression or equation with exact values.
Click here to preview your answer.

6. –/1 points Notes Question: RogaCalc1 3.9.014.
Question part
Points
Submissions
1
0/1
0/50
Total
0/1
 
A 6-ft man walks away from a 18-ft lamppost at a speed of 2 ft/s. (See Figure). Find the rate at which his shadow is increasing in length.
dl
dt
 =
Enter a mathematical expression or equation with exact values.
 ft/s


7. –/4 points Notes Question: RogaCalc1 3.9.026.
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
 
A particle moves counter-clockwise around the ellipse 16x2 + 36y2 = 25 (see figure).
Maple Generated Plot
(a) In which of the four quadrants is the derivative dx/dt positive? (Select all that apply.)



(b) Find a relation between dx/dt and dy/dt.
Enter a mathematical expression or equation with exact values.
Click here to preview your answer.

(c) At what rate is the x-coordinate changing when the particle passes the point (5/4, 0), if its y-coordinate is increasing at a rate of 7 ft/s?
Enter a mathematical expression or equation with exact values.
 ft/s

(d) What is dy/dt when the particle is at the top or bottom of the ellipse?
Enter a mathematical expression or equation with exact values.
 ft/s

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