Use x^2+2 in the Difference Quotient

AI Thread Summary
The discussion centers on solving the difference quotient for the function x^2 + 2. The initial attempt contained an error in expanding (x + h)^2, leading to incorrect simplifications. After correcting the expansion to x^2 + 2xh + h^2, the participant successfully derived the expression (2xh + h^2)/h. This simplifies to 2x + h, which aligns with one of the provided answer choices. The participant expresses gratitude for the assistance in resolving the mistake.
Tonik
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I took a placement test and blew it away. (I tested into calculus, best possible placement for this test.) Everything was rather simple except for this problem which I cannot seem to get right. Can someone show me where I'm going wrong here?

Homework Statement


Use x2+2 in the Difference Quotient.

Homework Equations


d55.gif

The Attempt at a Solution


(x+h)2+2-(x2+2)

x2+xh+h2+2-x2-2

[STRIKE]x2[/STRIKE]+xh+h2[STRIKE]+2[/STRIKE][STRIKE]-x2[/STRIKE][STRIKE]-2[/STRIKE]

(xh+h2)/h

(x[STRIKE]h[/STRIKE]+h[STRIKE]2[/STRIKE])/[STRIKE]h[/STRIKE]

x+h

This answer was not a given choice. Any ideas where I'm messing up?
(I'm sure I making stupid mistake somewhere that I'm overlooking)
 
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Tonik said:
x2+xh+h2+2-x2-2

There is an error in this line.
 
More specifically, you expanded (x + h)2 incorrectly. Also, you should use = between an expression on one line and the one on the following line.
 
pbandjay said:
There is an error in this line.

Mark44 said:
More specifically, you expanded (x + h)2 incorrectly. Also, you should use = between an expression on one line and the one on the following line.

ahh! okay...

x2+2xh+h2+2-x2-2

=

[STRIKE]x2[/STRIKE]+2xh+h2[STRIKE]+2-x2-2[/STRIKE]

=

2xh+h2/h

=

2x[STRIKE]h[/STRIKE]+h[STRIKE]2[/STRIKE]/[STRIKE]h[/STRIKE]

=

2x+h

That is the answer I chose since it was closest to my answer. You guys rock, thanks!
 

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