How do you use the squeeze theorem to show that #lim_(x to 0)x^4cos2x=0#?

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Answer 1 · 2017-04-17T20:08:13

Please see the explanation below.

We know:

#-1 leq cos2x leq 1#

By multiplying by #x^4#,

#-x^4 leq x^4cos2x leq x^4#

Since

#lim_(x to 0)(-x^4)=0# and #lim_(x to 0)x^4=0#,

by Squeeze Theorm,

#lim_(x to 0)x^4cos2x=0#

I hope that this was clear.