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Unformatted text preview: 2 x ) 1 /x . Solution: First write (12 x ) 1 /x = e (1 /x ) ln(12 x ) . We want to ﬁgure out what happens to this exponent as x goes to 0, i.e. we want to ﬁnd: lim x → ln(12 x ) x . 1 Now, as x → 0, we have ln(12 x ) → ln 1 = 0 and x → 0, so we can apply L’Hospital’s rule to this limit, and we get: lim x → ln(12 x ) x = lim x →2 12 x 1 = lim x →2 12 x =2 . So the exponent in our original expression e (1 /x ) ln(12 x ) goes to2 as x goes to 0. Hence lim x → (12 x ) 1 /x = lim x → e (1 /x ) ln(12 x ) = e2 . 2...
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This note was uploaded on 09/17/2011 for the course MATH 1A taught by Professor Wilkening during the Spring '08 term at Berkeley.
 Spring '08
 WILKENING
 Math, Calculus

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