Use x^2+2 in the Difference Quotient

In summary, the conversation discussed a placement test where the individual performed well and was placed in calculus. However, they were struggling with a problem involving the difference quotient using x2+2. They received help and discovered an error in their expansion, leading to the correct answer of 2x + h.
  • #1
Tonik
13
0
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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  • #2
Tonik said:
x2+xh+h2+2-x2-2

There is an error in this line.
 
  • #3
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.
 
  • #4
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!
 

1. What is the definition of the difference quotient?

The difference quotient is a mathematical expression used to calculate the average rate of change of a function over a given interval. It is typically represented as (f(x+h) - f(x))/h, where h represents the change in the input variable and f(x) represents the function.

2. Why is x^2+2 commonly used in the difference quotient?

X^2+2 is commonly used in the difference quotient because it is a simple and easy to understand function that can be used to demonstrate the concept of average rate of change. It also has a well-defined derivative, making it a useful function for calculus applications.

3. How do you calculate the difference quotient for x^2+2?

To calculate the difference quotient for x^2+2, you would use the formula (f(x+h) - f(x))/h and substitute in the given function. This would result in ((x+h)^2+2 - (x^2+2))/h, which can be simplified to (2xh + h^2)/h = 2x + h.

4. What is the significance of the difference quotient in calculus?

The difference quotient is significant in calculus because it is the foundation for the concept of derivatives, which are used to calculate instantaneous rate of change. It allows us to measure how a function changes over a small interval, which is essential in many real-world applications.

5. Can the difference quotient be used for functions other than x^2+2?

Yes, the difference quotient can be used for any function that has a well-defined derivative. It is a general formula that can be applied to any function to calculate the average rate of change over a given interval. However, the specific calculations may vary depending on the function being used.

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