How do you use L'hospital's rule to find the limit?

Answer 1

To use L'Hôpital's Rule to find the limit of a function, follow these steps:

  1. Identify the limit you want to evaluate.
  2. Check if the limit is of an indeterminate form, such as 0/0 or ∞/∞.
  3. If the limit is in an indeterminate form, apply L'Hôpital's Rule.
  4. Take the derivative of the numerator and the derivative of the denominator separately.
  5. Evaluate the limit of the derivatives.
  6. If the new limit is still in an indeterminate form, repeat steps 4 and 5 until you can evaluate the limit.
  7. Once you have found the limit of the derivatives, it is equivalent to the limit of the original function.
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Answer 2

l'Hopital's Rule

Indeterminate Form 1: #0#/#0#
If #lim_{x to a}f(x)=0# and #lim_{x to a}g(x)=0#,
then #lim_{x to a}{f(x)}/{g(x)}=\lim_{x to a}{f'(x)}/{g'(x)}#.
ex.) #lim_{x to 0}{sinx}/{x}#

by differentiating the numerator and the denominator separately,

#=lim_{x to 0}{cosx}/{1}=cos(0)=1#
Indeterminate Form 2: #infty#/#infty#
If #lim_{x to a}f(x)=pm infty# and #lim_{x to a}g(x)=pm infty#,
then #lim_{x to a}{f(x)}/{g(x)}=\lim_{x to a}{f'(x)}/{g'(x)}#.
ex.) #lim_{x to infty}{x}/{e^x}#

by differentiating the numerator and the denominator,

#=lim_{x to infty}{1}/{e^x}=1/infty=0#

Note: There are other indeterminate forms which can be turned into one of the above forms.

I hope that this was helpful.

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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.

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.

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.

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.

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