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How do you find #lim_(x->0^-)cosx/x#?

Answer 1

Ezekiel Alexander

See below.

#lim_(x->0^-)cos(x)/x=lim_(x->0^-)1/x * lim_(x->0^-)cos(x)#

#lim_(x->0^-)1/x=-oo#

#lim_(x->0^-)cos(x)=1#

#(lim_(x->0^-)1/x)*(lim_(x->0^-)cos(x))=-oo#

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Answer 2

Isabella Ackerman

To find the limit of cos(x)/x as x approaches 0 from the left side, we can use L'Hôpital's Rule. Taking the derivative of both the numerator and denominator, we get -sin(x)/1. Evaluating this at x=0, we find that the limit is equal to 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.

How do you find #lim_(x-&gt;0^-)cosx/x#?

How do you find #lim_(x->0^-)cosx/x#?