M MAM New member Joined Feb 4, 2012 Messages 6 Feb 14, 2012 #1 I need help solving the following: lim x^x x ->0+ lim (1 - (1/n))^n n -> infinity Any help would be much appreciated!!
I need help solving the following: lim x^x x ->0+ lim (1 - (1/n))^n n -> infinity Any help would be much appreciated!!
D daon2 Full Member Joined Aug 17, 2011 Messages 999 Feb 15, 2012 #2 Find these limit first: \(\displaystyle \displaystyle \lim_{x\to 0^+}\,\ln x^x = \lim_{x\to 0^+}\,x\ln x \) \(\displaystyle \displaystyle \lim_{n\to\infty}\,\ln\left(1-\frac{1}{n}\right )^n =\lim_{n\to\infty}\,n\ln\left(1-\frac{1}{n}\right )\) Last edited: Feb 15, 2012
Find these limit first: \(\displaystyle \displaystyle \lim_{x\to 0^+}\,\ln x^x = \lim_{x\to 0^+}\,x\ln x \) \(\displaystyle \displaystyle \lim_{n\to\infty}\,\ln\left(1-\frac{1}{n}\right )^n =\lim_{n\to\infty}\,n\ln\left(1-\frac{1}{n}\right )\)
