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Unformatted text preview: are diFerentiable functions such that lim x f ( x ) = 0 , lim x g ( x ) = 0 . Thus LHospitals 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 LHospitals rule has to be ap-plied 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 x-2 x-1 9 x 2 = 2 9 ....
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This note was uploaded on 02/14/2012 for the course MATH 408 K taught by Professor Clark,c.w./hoy,r.r during the Spring '08 term at University of Texas at Austin.
- Spring '08