L'Hospital's Rule or L'Hôpital's rule To Solve Indeterminate Forms 

L'Hospital's Rule or L'Hôpital's rule is the shortest method to solve any question which is in Indeterminate Forms like 0/0 ,∞/0,0/∞ etc.
L'Hospital's Rule or L'Hôpital's rule is very use full to solve questions in competitive exams like PET,AIEE,IIT etc. you can say this is shortcut to solve any question which is in indeterminate Forms.indeterminate Forms means you cannot determine value of any question by putting its limit value directly.

In L'Hospital's Rule or L'Hôpital's rule we differentiate numerator and denominator separately with respect of x where limit of x is given in question. 
In short we can say L'Hôpital's rule uses to solve limits questions involving indeterminate forms.
L’Hospital’s Rule tells us that if answer of any question of limit is an indeterminate form like 0/0 ,∞/0,0/∞ etc what all we need to do is first differentiate the numerator and second differentiate the denominator and then put the limit given in question.
L'Hospital's rule helps us to simplify an indeterminate form and transform into a determinate form. 
there are two types of Limit in category theory-1,Direct limit 2.Inverse limit.
In this video tutorial we can see how to use L’Hospital’s Rule 

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