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Math - College, section 1, Fall 2019
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Tan - Appl Calc for Man, Life, Soc Sci 10/e (Homework)

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 5 / 29

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

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

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Question

Points

1	2	3	4	5	6	7	8	9	10	11	12	13
1/1	1/1	1/1	1/1	–/2	–/4	–/1	–/8	–/1	1/1	–/2	–/3	–/3

Total

5/29 (17.2%)

Instructions

Applied Calculus for the Managerial, Life, and Social Sciences, 10th edition, by Soo Tan, published by Cengage Learning, balances applications, pedagogy, and technology to provide students the context they need to stay motivated in the course and interested in the material. Accessible for majors and non-majors alike, the text uses an intuitive approach that introduces abstract concepts through examples drawn from common, real-life experiences to which students can relate. It also draws applications from readers’ fields of interest. The WebAssign component for this title features an eBook, lecture videos and a Course Pack of ready-made assignments.

Question 1 contains a dynamic, randomized plot of the given scenario, while still retaining the relative position of key points.

Question 2 demonstrates equation grading that accepts any equivalent form of the line.

Question 3 has a half-open interval that must be entered using the correct notation at the endpoints. Also available for this question is a Watch-It link to a video example.

Question 4 has a Master It tutorial. If help features are enabled and the student selects the Master It, a different randomization is presented in a new window. The tutorial walks the student through detailed problem-solving steps using this new randomization. The student is then returned to the original problem.

Question 6 is an Expanded Problem version of Question 5 that requires the student to show answers to intermediate steps necessary to complete the problem. Look for .EP. problems to assign if you would like to pinpoint where students may have trouble in the solution process.

Question 7 features implicit differentiation grading that accepts any form of the correct derivative, such as rewriting the answer using the given expression for the square-root.

Question 8 is an in-depth application that preserves the "Interpret" parts of the question and utilizes list grading where the solutions can be entered in any order.

Question 9 illustrates indefinite integral grading that enforces proper use of C and absolute values. This question also contains a Watch-It video example.

Question 10 showcases a Master It tutorial involving a definite integral that requires substitution. If help features are enabled and the student selects the Master It, the tutorial walks the student through all necessary steps using a different randomization, then the student is returned to the original problem.

Question 11 exhibits an integral template where the student fills in the lower limit and integrand to model the given scenario. This question also has a Watch-It video.

Question 12 highlights a randomized data set for an application of linear regression. Numerical tolerance is handled throughout to account for rounding values in part (a).

Question 13 is an example of how series are handled, and also has a link to a Watch-It video. 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.

The answer key and solutions will display after the first submission for demonstration purposes. Instructors can configure these to display after the due date or after a specified number of submissions.

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. 1/1 points | Previous Answers TanApCalc10 1.3.036. My Notes

Planning a Grand Tour

A grand tour of four cities begins at City A and makes successive stops at cities B, C, and D before returning to City A. If the cities are located as shown in the following figure, find the total distance covered on the tour.

The x y coordinate plane is given; 4 points are connected by 4 segments, each with a directional arrow.
The first point is labeled A (0, 0) and is connected to B by a segment with a directional arrow that points to B.
The second point is labeled B (300, 400) and is connected to C by a segment with a directional arrow that points to C.
The third point is labeled C (−200, 1600) and is connected to D by a segment with a directional arrow that points to D.
The fourth point is labeled D (−200, 0) and is connected to A by a segment with a directional arrow that points to A.

3600

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2. 1/1 points | Previous Answers TanApCalc10 1.4.046. My Notes

Find an equation of the line that passes through the point (3, 4) and is perpendicular to the line

4x + 7y − 8 = 0.

y−4=74(x−3)

$webMathematica generated answer key$

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3. 1/1 points | Previous Answers TanApCalc10 2.1.034. My Notes

Find the domain of the function. (Enter your answer using interval notation.)

g(x) = 7(x − 1)^5/2

[[1,∞)]

$webMathematica generated answer key$

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4. 1/1 points | Previous Answers TanApCalc10 3.1.020.MI. My Notes

Find the derivative of the function f by using the rules of differentiation.

f(x) = (1 + 3x²)² + 3x³

f '(x) =

2(1+3x2)6x+9x2

$webMathematica generated answer key$

Solution or Explanation

f '(x) =

(1 + 3x²)² + 3x³

1 + 6x² + 9x⁴ + 3x³

= 12x + 36x³ + 9x²

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5. –/2 points TanApCalc10 3.4.027. My Notes

For the following demand equation compute the elasticity of demand and determine whether the demand is elastic, unitary, or inelastic at the indicated price.

x =

−

p + 13; p = 12

E(12) =

the demand is

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6. –/4 points TanApCalc10 3.4.027.EP. My Notes

Consider the following demand equation.

x =

−

p + 12

Let

x = f(p),

with price p. Find

f '(p).

f '(p) =

Find the elasticity of demand,

E(p).

E(p) =

Compute the elasticity of demand and determine whether the demand is elastic, unitary, or inelastic at the price

p = 9.

E(9) =

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7. –/1 points TanApCalc10 3.6.019. My Notes

Find

by implicit differentiation.

x + y

= 2x

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8. –/8 points TanApCalc10 4.2.098. My Notes

Google's Revenue

The revenue for a certain corporation from 2004 (t = 0) through 2008 (t = 4) is approximated by the function

R(t) = −0.2t³ + 1.72t² + 1.26t + 3.9 (0 ≤ t ≤ 4)

where

R(t)

is measured in billions of dollars.

(a)

Find

R'(t)

and

R''(t).

R'(t)	=
R''(t)	=

(b)

Show that

R'(t)

> 0 for all t in the interval (0, 4) and interpret your result. Hint: Use the quadratic formula.

Setting

R'(t) = 0

and solving for t gives

t =

(Enter all real number answers, whether or not they fall inside the defined interval. Round your answers to three decimal places. Enter your answers as a comma-separated list.)

Both roots lie the interval

(0, 4).

Because

R'(0) 0,

we conclude that

R'(t) 0

for all t in

(0, 4).

(c)

Find the inflection point of the graph of R. (Round your answer to two decimal places.)

t =

Interpret your result.

The corporation's revenue was always increasing between 2004 and 2008, and increased fastest in November 2006. The corporation's revenue went was increasing from the start of 2004 until November 2006, and decreasing from that point until the end of 2008. The corporation's revenue was always decreasing between 2004 and 2008, and decreased fastest in November 2006. The corporation's revenue went was decreasing from the start of 2004 until November 2006, and increasing from that point until the end of 2008. The corporation's revenue has been stable from the start of 2004 through to the end of 2008.

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9. –/1 points TanApCalc10 6.2.044. My Notes

Find the indefinite integral. Hint: Let

v = e^−u + 8u.

(Use C for the constant of integration. Remember to use absolute values where appropriate.)

e^−u − 8

e^−u + 8u

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10. 1/1 points | Previous Answers TanApCalc10 6.5.008.MI. My Notes

Evaluate the definite integral.

x² + 7

4−√7

$webMathematica generated answer key$

Solution or Explanation

Let

u = x² + 7

so that

du = 2x dx

x dx =

du.

Also, if

x = 0,

then

u = 7

and if

x = 3,

then

u = 16.

x² + 7

u^1/2

	16
	7

4 −

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11. –/2 points TanApCalc10 6.6.045. My Notes

Oil Production Shortfall

Energy experts disagree about when global oil production will begin to decline. In the following figure, the function f gives the annual world oil production in billions of barrels from 1980 to 2050, according to the Department of Energy projection. The function g gives the world oil production in billions of barrels per year over the same period, according to longtime petroleum geologist Colin Campbell.†Source: U.S. Department of energy; Colin Campbell Find an expression in terms of the definite integrals involving f(t) and g(t), giving the shortfall S in the total oil production over the period in question heeding Campbell's dire warnings.

On the coordinate plane the horizontal axis is labeled t (year) and the vertical axis is labeled y (billions of barrels). Two curves, f(t) and g(t), each with two parts, are graphed.
The first part of f(t) is a curve, enters the window at y = 21 on the positive y axis, goes up and right becoming more steep, and ends at the point (2040, 53).
The second part of f(t) is a curve, begins at the point (2040, 53), goes horizontally right, and ends at the point (2050, 19).
The first part of g(t) is a curve, enters the window at y = 21 on the positive y axis, goes up and right becoming more steep, and ends at the point (2010, 30).
The second part of g(t) is a curve, begins at the point (2010, 30), goes down and right becoming less steep, and ends at the point (2050, 10).

S =

2050

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12. –/3 points TanApCalc10 8.4.026. My Notes

Global Defense Spending

Suppose the following table gives the projected global defense spending (in trillions of dollars) from the beginning of 2008

(t = 0)

through 2015

(t = 7).

Year, x	0	1	2	3	4	5	6	7
Sales, y	1.25	1.26	1.29	1.3	1.53	1.68	1.79	1.88

(a)

Find an equation of the least-squares line y for these data. (Round numerical values to three decimal places.)

y =

(b)

Use the result of part (a) to estimate the rate of change in the projected global defense spending from 2008 through 2015. (Round your answer to three decimal places.)

$ trillion/yr

(c)

Assuming that the trend continues, what will the global spending on defense be in 2018? (Round your answer to two decimal places.)

$ trillion

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13. –/3 points TanApCalc10 11.5.022. My Notes

Find the Taylor series of the function at the indicated number.

f(x) =

x + 1

; x = 0

∞

n = 0

Give its radius of convergence R.

R =

Give its interval of convergence. (Enter your answer using interval notation.)

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