Limit Problem

  • Thread starter Flamingo
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  • #1
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Main Question or Discussion Point

I'm having trouble with this one. How do I get h out of the denominator?

[tex]lim_{h\rightarrow0}\left(\frac{\frac{1}{(a+h)^{2}}-\frac{1}{x^{2}}}{h}\right)[/tex]

[tex]lim_{h\rightarrow0}\left(\frac{1}{h(a+h)^2}-\frac{1}{hx^{2}}\right)[/tex]

[tex]lim_{h\rightarrow0}\left(\frac{hx^2-h(a+h)^2}{h^2x^2(a+h)^2}\right)[/tex]

[tex]lim_{h\rightarrow0}\left(\frac{x^2-(a+h)^2}{hx^2(a+h)^2}\right)[/tex]

I keep getting a divide by zero. Am I wrong?
 

Answers and Replies

  • #2
1,631
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I'm having trouble with this one. How do I get h out of the denominator?

[tex]lim_{h\rightarrow0}\left(\frac{\frac{1}{(a+h)^{2}}-\frac{1}{x^{2}}}{h}\right)[/tex]

[tex]lim_{h\rightarrow0}\left(\frac{1}{h(a+h)^2}-\frac{1}{hx^{2}}\right)[/tex]

[tex]lim_{h\rightarrow0}\left(\frac{hx^2-h(a+h)^2}{h^2x^2(a+h)^2}\right)[/tex]

[tex]lim_{h\rightarrow0}\left(\frac{x^2-(a+h)^2}{hx^2(a+h)^2}\right)[/tex]

I keep getting a divide by zero. Am I wrong?
Are you trying to find the derivative of 1/x^2 using the def. of the derivative???????
 
  • #3
19
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that should be an 'a' where it is an 'x', sorry.
 
  • #4
19
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lol, a=x.
 
  • #5
19
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and, yes, I am suppose to solve it using algebra.
 
  • #6
1,631
4
I'm having trouble with this one. How do I get h out of the denominator?

[tex]lim_{h\rightarrow0}\left(\frac{\frac{1}{(a+h)^{2}}-\frac{1}{x^{2}}}{h}\right)[/tex]

[tex]lim_{h\rightarrow0}\left(\frac{1}{h(a+h)^2}-\frac{1}{hx^{2}}\right)[/tex]

[tex]lim_{h\rightarrow0}\left(\frac{hx^2-h(a+h)^2}{h^2x^2(a+h)^2}\right)[/tex]

[tex]lim_{h\rightarrow0}\left(\frac{x^2-(a+h)^2}{hx^2(a+h)^2}\right)[/tex]

I keep getting a divide by zero. Am I wrong?
i do not know whether u did the algebra good up to the last part, i won't be checking that. here at the last part you can rearrange the numerator like this

: a^2-(a+h)^2=(a-a-h)(a+a+h)=-h(2a+h)
so you will get rid of the h on the denominator.
 
  • #7
19
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very clever, thanks
 

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