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What is the limit as x approaches infinity of #sin(x)#?

Answer 1

As #x# approaches infinity, the #y#-value oscillates between #1# and #-1#; so this limit does not exist.

Thus, the answer is it DNE (does not exist).

One good rule to have while solving these problems is that generally, if there is no #x# in the denominator at all, then the limit does not exist.

Example:

#lim_(x->oo)sinx=DNE#

#lim_(x->oo)(sinx)/(x)=0# (Squeeze Theorum)

This is the same question as below:

How do you show the limit does not exist #lim_(x->oo)sin(x)# ?

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Answer 2

Isabella Ackerman

The limit as x approaches infinity of sin(x) does not exist.

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Answer from HIX Tutor

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.