- #1
nobahar
- 497
- 2
Hello!
This is another conceptual understanding question. Any help is appreciated.
I want to solve the following:
The limit as x -> 1 of:
[tex]\frac{x^{10}-1}{x^2-1}[/tex]
So I divide the numerator and denominator by x-1 and then find the derivative of them separately with respect to x. Then take the ratio of the two derivatives.
My question is: why divide by x-1?
Is it so that it fits the form of the following derivative?:
The limit as x -> x0 of:
[tex]\frac{f(x_0 + dx) - f(x_0)}{x-x_0}[/tex]
[tex]\frac{x^{10}-1 - (1^10-1)}{x-1}[/tex]
So I'm assuming x0= 1 and x(^10) -1 is a f(x)?
Thanks in advance. I can elaborate if it's not clear, I was more worried about the Latex not working!
This is another conceptual understanding question. Any help is appreciated.
I want to solve the following:
The limit as x -> 1 of:
[tex]\frac{x^{10}-1}{x^2-1}[/tex]
So I divide the numerator and denominator by x-1 and then find the derivative of them separately with respect to x. Then take the ratio of the two derivatives.
My question is: why divide by x-1?
Is it so that it fits the form of the following derivative?:
The limit as x -> x0 of:
[tex]\frac{f(x_0 + dx) - f(x_0)}{x-x_0}[/tex]
[tex]\frac{x^{10}-1 - (1^10-1)}{x-1}[/tex]
So I'm assuming x0= 1 and x(^10) -1 is a f(x)?
Thanks in advance. I can elaborate if it's not clear, I was more worried about the Latex not working!
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