# What's the limit of #(x^n-a^n)/(x-a)# as #x# approaches #a# , using the derivate number which is #f'(a)# ?

Please see below.

If I understand it, I think I need to point out that

That is:

We also know, by the power rule for derivatives,

We can conclude that

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The limit of (x^n-a^n)/(x-a) as x approaches a is n*a^(n-1).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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- What is the limit of #(8-(7y^2))/((2y^2)+9y)# as x goes to infinity?
- How do you find the limit of #ln(lnt)# as #t->oo#?
- What is the limit of #(x^2)(e^x)# as x goes to negative infinity?

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