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is there any proof or derivation of L hospital rule

is there any proof or derivation of L hospital rule

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1 Answers

SAGAR SINGH - IIT DELHI
879 Points
11 years ago

Dear vikash,

Let lim stand for the limit  lim_(x->c), lim_(x->c^-), lim_(x->c^+), lim_(x->infty), or lim_(x->-infty), and suppose that lim f(x) and lim g(x) are both zero or are both +/-infty. If

 lim(f^'(x))/(g^'(x))

has a finite value or if the limit is +/-infty, then

 lim(f(x))/(g(x))=lim(f^'(x))/(g^'(x)).

Historically, this result first appeared in l'Hospital's 1696 treatise, which was the first textbook on differential calculas.

 

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Sagar Singh

B.Tech IIT Delhi

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