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What is the limit of #sin^4(x)/x^0.5# as x goes to infinity?

Answer 1

Samantha Adkison

It is #0#

#0 <= sin^4x <= 1# for all #x#

#x^0.5 > 0# for #x > 0#, so we can divide in the inequality without changing the directions of the inequalities.

#0 <= sin^4x/x^0.5 <= 1/x^0.5# for all #x#

We note that #lim_(xrarroo) 0 = lim_(xrarroo) 1/x^0.5 = 0#,

so, by the squeeze theorem, #lim_(xrarroo) sin^4x/x^0.5 = 0#

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Answer 2

Elijah Abram

The limit of sin^4(x)/x^0.5 as x goes to infinity is 0.

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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.