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# Calculus

What is 'L hospital 's rule' and please mention the proof?

Note by Goutam Narayan
2 years, 9 months ago

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Hey...do check the wikipedia page ...http://en.wikipedia.org/wiki/L'Hôpital's_rule.....do get back if there is any problem you r facing · 2 years, 7 months ago

L hospital's rule is used to solve indeterminate forms of the type 0/0 ,infinity/infinity type .Put simply,if the two functions f(x) &g(x) is defined in an interval containing' a ',except possibility at' a' such that lim f(x) =0 &lim g(x) =0 x turns to a x turns to a but the derivatives f'(x)&g'(x) has finite limit at x=a then the theorem state that lim f(x)/g(x) = lim f'(x)/g'(x) x turns to a x turns to a

for eg ;evaluate lim x^2 -4/x-2 ( form 0/0) x turns to 2 let f(x)=x^2 -4 , f'(x)= 2x g(x) = x-2 g'(x) =1 hence lim x^2 -4/x-2= 2x/1 = 4 x turns to 2 for better reference , clarifications and proof u can refer CALCULUS by Anton ,Bivens and Stephen Davis · 2 years, 9 months ago

L hospital's rule is used to solve indeterminate forms of the type 0/0 ,infinity/infinity type .Put simply,if the two functions f(x) &g(x) is defined in an interval containing' a ',except possibility at' a' such that lim f(x) =0 &lim g(x) =0
x turns to a x turns to a
but the derivatives f'(x)&g'(x) has finite limit at x=a
then the theorem state that lim f(x)/g(x) = lim f'(x)/g'(x) x turns to a x turns to a

for eg ;evaluate lim x^2 -4/x-2 ( form 0/0) x turns to 2
let f(x)=x^2 -4 , f'(x)= 2x
g(x) = x-2 g'(x) =1 hence lim x^2 -4/x-2= 2x/1 = 4 x turns to 2
for better reference , clarifications and proof u can refer CALCULUS by Anton ,Bivens and Stephen Davis · 2 years, 9 months ago