# What is #lim_(x->0) ((1+x)^n-1)/x# ?

Hence, L'Hopital's rule applies.

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The limit of ((1+x)^n-1)/x as x approaches 0 is n.

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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.

- What is the limit of #(x/(x+1))^x# as x approaches infinity?
- How do you prove that the #lim_(xrarr3) (4x-5)=7# using the formal definition of a limit?
- What is the limit of #(e^(−7x))cos x# as x approaches infinity?
- How do you determine the limit of #(x+1)/(x^2(x+4))# as x approaches 0?
- What are the removable and non-removable discontinuities, if any, of #f(x)=(x+3)/((x-4)(x+3))#?

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