Proof of L’Hospital’s Rule - MathCs Server

Theorem: Suppose f ' (x) , g ' (x) exist and g' x ≠ 0 for all x in an interval ( a , b ] . If lim x → a + f x =0= lim x → a + g x and lim x → a + f ' x g ' x exists then lim x → a + f x g x = lim x → a + f ' x g ' x . Proof: We may assume that . f a =0=g(a) (since the limit is not affected by the value of the function at a ). Also g ... ................
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