How to Solve a Limit Problem with a Denominator of Zero?

[Flamingo]

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

$$lim_{h\rightarrow0}\left(\frac{\frac{1}{(a+h)^{2}}-\frac{1}{x^{2}}}{h}\right)$$

$$lim_{h\rightarrow0}\left(\frac{1}{h(a+h)^2}-\frac{1}{hx^{2}}\right)$$

$$lim_{h\rightarrow0}\left(\frac{hx^2-h(a+h)^2}{h^2x^2(a+h)^2}\right)$$

$$lim_{h\rightarrow0}\left(\frac{x^2-(a+h)^2}{hx^2(a+h)^2}\right)$$

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

 

[sutupidmath]

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

$$lim_{h\rightarrow0}\left(\frac{\frac{1}{(a+h)^{2}}-\frac{1}{x^{2}}}{h}\right)$$

$$lim_{h\rightarrow0}\left(\frac{1}{h(a+h)^2}-\frac{1}{hx^{2}}\right)$$

$$lim_{h\rightarrow0}\left(\frac{hx^2-h(a+h)^2}{h^2x^2(a+h)^2}\right)$$

$$lim_{h\rightarrow0}\left(\frac{x^2-(a+h)^2}{hx^2(a+h)^2}\right)$$

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??

 

[Flamingo]

that should be an 'a' where it is an 'x', sorry.

 

[Flamingo]

lol, a=x.

 

[Flamingo]

and, yes, I am suppose to solve it using algebra.

 

[sutupidmath]

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

$$lim_{h\rightarrow0}\left(\frac{\frac{1}{(a+h)^{2}}-\frac{1}{x^{2}}}{h}\right)$$

$$lim_{h\rightarrow0}\left(\frac{1}{h(a+h)^2}-\frac{1}{hx^{2}}\right)$$

$$lim_{h\rightarrow0}\left(\frac{hx^2-h(a+h)^2}{h^2x^2(a+h)^2}\right)$$

$$lim_{h\rightarrow0}\left(\frac{x^2-(a+h)^2}{hx^2(a+h)^2}\right)$$

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.

 

[Flamingo]

very clever, thanks