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lim (1-2x)^1/x
x->0

Thanks

2007-10-22 13:06:44 · 2 answers · asked by Smokey. 6 in Science & Mathematics Mathematics

2 answers

y=(1-x)^(1/x)
ln (y) =lim x->0[(1/x) ln (1-2x)]
=lim x->0 [ln(1-2x) / x] 0/0 form
differentiate top and bottom
lim x->0 [-2/(1-2x)/1]=-2
ln y ->-2
y -> e^(-2)

2007-10-22 13:56:33 · answer #1 · answered by cidyah 7 · 0 0

The basic idea is that the lim(f/g) will often be the limit of (f'/g'). The reason that's true is because if you take the definition of the derivative in both the quotient and denominator, the (x-h) or (x-x0) terms cancel.

2007-10-22 16:02:02 · answer #2 · answered by Curt Monash 7 · 0 0

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