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What are Special Limits Involving #y=sin(x)#?

Answer 1

One of some useful limits involving #y=sin x# is #lim_{x to 0}{sin x}/{x}=1#. (Note: This limit indicates that two functions #y=sin x# and #y=x# are very similar when #x# is near #0#.)

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Answer 2

Isabella Ackerman

Special limits involving ( y = \sin(x) ) are:

( \lim_{x \to 0} \frac{\sin(x)}{x} = 1 )
( \lim_{x \to \infty} \sin(x) ) and ( \lim_{x \to -\infty} \sin(x) ) do not exist.
( \lim_{x \to \infty} \frac{\sin(x)}{x} = 0 )
( \lim_{x \to -\infty} \frac{\sin(x)}{x} = 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.