# Evaluate the limit #lim_(x rarr 0^+) (1+1/x)^x #?

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# lim_(x rarr 0^+) (1+1/x)^x = 1 #

We seek:

As the log function is monotonic we can tak logs of both sides to get:

Thus:

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The limit of (1+1/x)^x as x approaches 0 from the positive side is equal to e, where e is the mathematical constant approximately equal to 2.71828.

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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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- How do you find the limit of #sqrt(x^2 + x + 1) / x# as x approaches infinity?
- How do you find the limit of # [-1/5(1-(1/x)^(4/5)]# as x approaches infinity?
- How do you remove a removable discontinuity?

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