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" ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^