# What is #lim_(xrarroo) (e^xsin(1/x))/x #?

The limit does not exist.

The limit does not exist because polynomial growth (denominator) is slower than exponential growth (numerator). (https://tutor.hix.ai)

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The limit of (e^xsin(1/x))/x as x approaches infinity is 0.

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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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