SOLVED:Suppose f is a positive function. If lim_{x\to a} f(x) = 0 and lim_{x\to a} g(x) = \infty , show that \displaystyle \lim_{x\to a} [f(x)]^{g(x)} = 0 This shows that 0^{\infty} is not an indeterminate form.

Name: suppose f is a positive function if lim_xto a fx 0 and lim_xto a gx infty show that displaystyle lim
Uploaded: 2019-11-15
Duration: 1 min 12 s
Channel: Numerade
Description: Suppose $ f $ is a positive function. If $ lim_{x\to a} f(x) = 0 $ and $ lim_{x\to a} g(x) = \infty $, show that $$ \displaystyle \lim_{x\to a} [f(x)]^{g(x)} = 0 $$ This shows that $ 0^{\infty} $ is not an indeterminate form.