Larson and Edwards - Calculus ET 6/e (Homework)

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 18 / 18

Due : Sunday, January 27, 2030 00:00 EST

Last Saved : n/a Saving... ()

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Points

1	2	3	4	5	6	7	8
2/2	8/8	1/1	3/3	1/1	1/1	1/1	1/1

Total

18/18 (100.0%)

Instructions

Create your course assignments by selecting questions from our bank of end-of-section exercises, as well as enhanced interactive examples with videos.

Students can view and hear additional instruction through the 2-5 minute Watch It links. Students will also find helpful links to online excerpts from their textbook, tutorials, and videos.

Every problem includes a link to the appropriate section of a complete interactive eBook, (also available through a dynamic table of contents from the student's WebAssign homepage), allowing students to highlight and take notes as they read.

Many problems include detailed stepped-out solutions, available to students at each instructor's discretion. The solutions use the same algorithmic values assigned in the problem, further driving problem-solving mastery.

This book also includes a Personal Study Plan (PSP). Once PSP is enabled for your course, your students can use chapter and section assessments to gauge their mastery of the material and generate individualized study plans that include various online, interactive multimedia resources.

- relevant textbook pages

- videos of worked examples

- tutorials

In this assignment we present several textbook question types found in Calculus: Early Transcendental Functions 6/e by Ron Larson and Bruce H. Edwards published by Cengage Learning.

Click here for a list of all of the questions coded in WebAssign. This demo assignment allows many submissions and allows you to try another version of the same question for practice wherever the problem has randomized values.

Assignment Submission

For this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes if you submit or change the answer.

Assignment Scoring

Your last submission is used for your score.

1. 2/2 points | Previous Answers LarCalcET6 3.1.053.MI. My Notes

Identify a function f that has the given characteristics. Then sketch the function.

f(3) = 18

f '(x) = 4, −∞ < x < ∞

f(x) =

4x+6

0,0

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

-10

-5

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2. 8/8 points | Previous Answers LarCalcET6 3.2.060.MI.SA. My Notes

This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.

Determine the point(s) (if any) at which the graph of the function has a horizontal tangent line.

y = x² + 8

Step 1

We are asked to find any points on the function that have a horizontal tangent line. In other words, the slope of the tangent line is zero

zero

Step 2

Since we want to know where the tangent line is zero, we need to find all points where the derivative is zero. Start by finding the derivative of the equation. To do this, we use a combination of the basic differentiation rules. First take the derivative of both sides of the equation.

x² + 8

$$x2+8

$webMathematica generated answer key$

Step 3

Next, apply the Sum Rule to separate the right side into the sum of two derivatives.

[x² + 8]

$$x2

$webMathematica generated answer key$

[8]

Step 4

Now use the Power Rule and the Constant Multiple Rule to determine the derivatives.

[x²] +

[8]

$$2x

$webMathematica generated answer key$

Step 5

Now that we have the derivative, we need to set it equal to zero and solve for x.

= 2x = 0

x = 0

Step 6

We now have the x-coordinates of the point where the derivative is zero. To find the y-coordinate, substitute zero for x in the original function.

y	=	x² + 8
	=	0 0 ² + 8
	=	8 8

Step 7

We now have both the x- and y-coordinate for the point where the tangent line is horizontal to our function.

The point is

(x, y) =

0,8

$webMathematica generated answer key$

You have now completed the Master It.

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3. 1/1 points | Previous Answers LarCalcET6 3.3.012.MI. My Notes

Use the Quotient Rule to differentiate the function.

f(t) =

cos(t)

t⁵

f '(t) =

−tsin(t)+5cos(t)t6

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4. 3/3 points | Previous Answers LarCalcET6 3.4.041. My Notes

Find the slope of the tangent line to the sine function at the origin.

(a)

(b)

Compare these values with the number of complete cycles in the interval [0, 2π]. What can you conclude about the slope of the sine function

sin ax

at the origin?

The slope of

sin ax

at the origin is

a

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5. 1/1 points | Previous Answers LarCalcET6 3.4.076.MI. My Notes

Find the derivative.

y = ln

3 + e^x

3 − e^x

y' =

6ex9−e2x

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6. 1/1 points | Previous Answers LarCalcET6 3.4.VE.002. My Notes

Watch the video below then answer the question.

cos(x²) = (cos(x))².

True False

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7. 1/1 points | Previous Answers LarCalcET6 3.5.017. My Notes

Find

dy/dx

by implicit differentiation.

x² − 8 ln y + y² = 14

−2xy2y2−8

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8. 1/1 points | Previous Answers LarCalcET6 3.7.043. My Notes

A security camera is centered 20 feet above a 120-foot hallway (see figure). It is easiest to design the camera with a constant angular rate of rotation, but this results in a variable rate at which the images of the surveillance area are recorded. So, it is desirable to design a system with a variable rate of rotation and a constant rate of movement of the scanning beam along the hallway. Find a model for the variable rate of rotation if

|dx/dt| = 8

feet per second.

dθ

2cos2(θ)5

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Larson and Edwards - Calculus ET 6/e (Homework)

Current Score : 18 / 18

Due : Sunday, January 27, 2030 00:00 EST

Last Saved : n/a Saving... ()

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