Unformatted text preview: are diFerentiable functions such that lim x → f ( x ) = 0 , lim x → g ( x ) = 0 . Thus L’Hospital’s rule can be applied, so lim x → f ( x ) g ( x ) = lim x → f ( x ) g ( x ) . But lim x → f ( x ) = 0 , lim x → g ( x ) = 0 , in which case L’Hospital’s rule has to be applied again. Consequently, lim x → f ( x ) g ( x ) = lim x → f 00 ( x ) g 00 ( x ) . Since f 00 ( x ) = 4 e 2 x , g 00 ( x ) = 18 , it now follows that lim x → e 2 x2 x1 9 x 2 = 2 9 ....
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 Spring '08
 CLARK,C.W./HOY,R.R
 Calculus, Limit, lim, x→0

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