QUERY 9

course MTH 271

10/04, 1520

`questionNumber 90000 **** Query problem 1.4.06 diff quotient for x^2-x+1 **** What is the simplified form of the difference quotient for x^2-x+1?

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RESPONSE -->

f(x)=x^2 - x + 1

[f(x + 'dx) - f(x)]/'dx

(x + 'dx)^2 - (x + 'dx) +1

f(x + 'dx)=x^2 + 2x'dx + 'dx^2 - x - 'dx +1

[(x^2 + 2x'dx + 'dx^2 -x -'dx + 1) - (x^2 -x +1)]/'dx

2x'dx + 'dx^2 - 'dx/ 'dx

'dx(2x + 'dx -1)/ 'dx

2x + 'dx -1

confidence rating: 2

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22:29:12

`questionNumber 90000

1.4.40 (was 1.4.34 f+g, f*g, f/g, f(g), g(f) for f=x/(x+1) and g=x^3

the requested functions and the domain and range of each.

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RESPONSE -->

A. F(x) + g(x)

(x/(x+1)) + x^3

(x/(x+1)) +x^3((x+1)/(x+1))

(x/(x+1)) + (x^4 + X^3)/(x+1)

x + x^4 + x^3 / (x + 1)

x(1 + x^3 + x^2) / (x+1)

B. f(x) * g(x)

(x/(x+1)) * x^3

x^4 / (x +1)

C. f(x)/g(x)

(x/(x + 1)) / x^3

(x/(x+1) * (1/x^3)

x/(x^4 + x^3)

x/(x(x^3 + x^2))

1/(x^3 + x^2)

D. f(g(x))

x^3 / (x^3 +1)

E. g(f(x))

(x/(x+1))^3

x^3 / (x^3 + 3x^2 + 3x + 1)

confidence rating: 3

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22:34:57

`questionNumber 90000

1.4.66 (was 1.4.60 graphs of |x|+3, -.5|x|, |x-2|, |x+1|-1, 2|x| from graph of |x|

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RESPONSE -->

|x| + 3 absolute value of x, starting at (0,3)

-.5|x| absolute value of x turned upside down (i.e, opening toward negative y values), also 2x the width of |x|

|x-2| absolute value of x shifted to start at (2,0)

|x+1| - 1 absolute value of x starting at (-1.-1)

2|x| absolute value of x that is 1/2 the width of |x|

confidence rating: 1

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22:37:05

`questionNumber 90000

1.4.71 (was 1.4.64 find x(p) from p(x) = 14.75/(1+.01x)

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RESPONSE -->

p=14.75/ (1 + .01x)

1 + .01x= 14.75/p

.01x=(14.75/p) -1

x=(1475/p) -100

confidence rating: 2

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22:38:43

`questionNumber 90000

What is the x as a function of p, and how many units are sold when the price is $10?

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RESPONSE -->

x=(1475/p) -100

p=10

x(10)=(1475/10) -100

x(10)=47.5 or approximately 48 units

confidence rating: 2"

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From what I can see this looks good; however see my previous notes on the need to include given solutions and self-critiques.