Limit and inverse function

**Sally_Math** · February 3rd 2009, 08:04 PM

I have two questions:-

simplify the expression
cos(tan inverse(x))

evaluate the limit
lim(as x>infinty) (xe^(1/x)-x)

**javax** · February 3rd 2009, 10:26 PM

Originally Posted by Sally_Math

evaluate the limit
lim(as x>infinty) (xe^(1/x)-x)

$<br /> \lim_{x\to\infty}{x e^{\frac{1}{x}}-x}=\lim_{x \to \infty}{x(e^{\frac{1}{x}}-1)} = \lim_{x \to \infty}{\frac{e^{\frac{1}{x}}-1}{\frac{1}{x}}}$

Now you can apply L'Hospital's rule $\lim_{x \to \infty}{\frac{(e^{\frac{1}{x}}-1)'}{(\frac{1}{x})'}} = \lim_{x \to \infty}{e^{\frac{1}{x}}} = 1$

Thread: Limit and inverse function

LinkBack

Thread Tools

Display

Limit and inverse function

Similar Math Help Forum Discussions

Multiple solutions for limit of an inverse function without a calculator

Inverse function, in terms with another inverse function

Limit, Limit Superior, and Limit Inferior of a function

inverse limit

Inverse of function WITH a limit??

Search Tags