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MTH 271
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** Question Form_labelMessages **
Mod 9 query
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009. `query 9
Question: `q **** 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?
Your solution:
f(x+`dx) - f(x) ] / `dx
(x+`dx)^2 - (x+`dx) + 1 - (x^2 - x + 1) ] / `dx. [ x^2 + 2 x `dx + `dx^2 - x - `dx + 1 - x^2 + x - 1 ] / `dx}[ 2 x `dx - `dx + `dx^2 ] / `dx
2 x - 1 + `dx.
2 * 2 - 1 + `dx = 3 + `dx
Confidence Rating:2
Given Solution:
`a The difference quotient would be
[ f(x+`dx) - f(x) ] / `dx =
[ (x+`dx)^2 - (x+`dx) + 1 - (x^2 - x + 1) ] / `dx. Expanding the squared term, etc., this is
[ x^2 + 2 x `dx + `dx^2 - x - `dx + 1 - x^2 + x - 1 ] / `dx, which simplifies further to
}[ 2 x `dx - `dx + `dx^2 ] / `dx, then dividing by the `dx we get
2 x - 1 + `dx.
For x = 2 this simplifies to 2 * 2 - 1 + `dx = 3 + `dx. **
Self-critique (if necessary):
Self-critique Rating:
Question: `q1.4.40 (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.
Your solution:
`a (f+g)(x) = x / (x + 1) + x^3 = (x^4 + x^3 + x) / (x + 1). Domain: x can be any real number except -1.
(f * g)(x) = x^3 * x / (x+1) = x^4 / (x+1). Domain: x can be any real number except -1.
(f / g)(x) = [ x / (x+1) ] / x^3 = 1 / [x^2(x+1)] = 1 / (x^3 + x^2), Domain: x can be any real number except -1 or 0
f(g(x)) = g(x) / (g(x) + 1) = x^3 / (x^3 + 1). Domain: x can be any real number except -1
g(f(x)) = (f(x))^3 = (x / (x+1) )^3 = x^3 / (x+1)^3. Domain: x can be any real number except -1 **
Confidence Rating:1
Given Solution:
`a (f+g)(x) = x / (x + 1) + x^3 = (x^4 + x^3 + x) / (x + 1). Domain: x can be any real number except -1.
(f * g)(x) = x^3 * x / (x+1) = x^4 / (x+1). Domain: x can be any real number except -1.
(f / g)(x) = [ x / (x+1) ] / x^3 = 1 / [x^2(x+1)] = 1 / (x^3 + x^2), Domain: x can be any real number except -1 or 0
f(g(x)) = g(x) / (g(x) + 1) = x^3 / (x^3 + 1). Domain: x can be any real number except -1
g(f(x)) = (f(x))^3 = (x / (x+1) )^3 = x^3 / (x+1)^3. Domain: x can be any real number except -1 **
Self-critique (if necessary):
Self-critique Rating:
Question: `q1.4.71 (was 1.4.64 find x(p) from p(x) = 14.75/(1+.01x)
Your solution:
`a p = 14.75 / (1 + .01 x).
(1 + .01 x) * p = 14.75
1 + .01 x = 14.75 / p
1 x = 14.75 / p - 1
= 1475 / p - 100
= (1475 - 100 p) / p.
If p = 10 then x = (1475 - 100 p) / p = (1475 - 100 * 10) / 10 = 475 / 10 = 47.5 **
Confidence Rating:2
Given Solution:
`a p = 14.75 / (1 + .01 x). Multiply both sides by 1 + .01 x to get
(1 + .01 x) * p = 14.75. Divide both sides by p to get
1 + .01 x = 14.75 / p. Subtract 1 from both sides to get
1 x = 14.75 / p - 1. Multiply both sides by 100 to get
= 1475 / p - 100. Put the right-hand side over common denominator p:
= (1475 - 100 p) / p.
If p = 10 then x = (1475 - 100 p) / p = (1475 - 100 * 10) / 10 = 475 / 10 = 47.5 **
Self-critique (if necessary):
Self-critique Rating:
Question: `qWhat is the x as a function of p, and how many units are sold when the price is $10?
Your solution:
x = (1475 - 100 p) / p
= (1475 - 100 * 10) / 10
= 475 / 10
= 47.5
x
Given Solution:
`a If p = 10 then x = (1475 - 100 p) / p = (1475 - 100 * 10) / 10 = 475 / 10 = 47.5 **
Self-critique (if necessary):
Self-critique Rating
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