Use x^2+2 in the Difference Quotient

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Homework Help Overview

The problem involves using the expression x² + 2 in the context of the difference quotient, which is a fundamental concept in calculus. The original poster expresses difficulty in arriving at the correct form of the difference quotient for the given expression.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to simplify the difference quotient but seems to struggle with the expansion of (x + h)². Some participants point out errors in the expansion and suggest using equal signs to clarify the steps taken.

Discussion Status

Participants are actively identifying errors in the original poster's work and providing corrections. There is a collaborative effort to clarify the steps involved in the difference quotient, though no consensus on the final answer has been reached.

Contextual Notes

The discussion includes a focus on the proper expansion of polynomial expressions and the notation used in mathematical writing. The original poster expresses concern about potentially making a simple mistake, indicating a learning process in understanding the difference quotient.

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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