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

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Jun 4, 2017

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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