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What is an example l'hospital's rule?

Answer 1

Elijah Abram

Hello,

Determine #lim_{x->0} sin(x)/sinh(x)#.

The L'Hospital's rule says that it's #lim_{x->0} (sin'(x))/(sinh'(x)) = lim_{x->0} cos(x)/cosh(x) = 1/1=1#.

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Answer 2

Isaiah Allen

An example of l'Hôpital's rule is when you have a limit of the form 0/0 or ∞/∞. For instance, if you have the limit of (x^2 - 4)/(x - 2) as x approaches 2, you can apply l'Hôpital's rule by taking the derivative of the numerator and denominator separately. In this case, the derivative of x^2 - 4 is 2x, and the derivative of x - 2 is 1. Then, you can evaluate the limit of the derivatives, which is 2, to find that the original limit is also 2.

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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.