Question

$lim_{x to o} (1+3x)^{ frac{-1}{2x}}$

Answer 1

$lim_{x to 0} (1+3x)^{ frac{-1}{2x}}=lim_{x to 0} (1+3x)^{ frac{-1}{2x}*3x*frac{1}{3x}}=e^{lim_{x to 0}frac{-1*3x}{2x}}=\\=e^frac{-3}2}=frac{1}{sqrt{e^3}}$