Question

Tfraiz.

Answer 1

o.O

Answer 2

\[\lim_{x \rightarrow 0}(\frac{1}{x})^x\]
Take the ln and you get:
\[\lim_{x \rightarrow 0} x \ln(\frac{1}{x})=\lim_{x \rightarrow 0}\frac{\ln(\frac{1}{x})}{\frac{1}{x}}\]
Differentiating top and bottom you get:
\[\lim_{x \rightarrow 0}\frac{\frac{\frac{-1}{x^2}}{\frac{1}{x}}}{\frac{-1}{x^2}}\]
Simplifying it you get:
\[\lim_{x \rightarrow 0}\frac{\frac{-1}{x}}{\frac{-1}{x^2}}=\lim_{x \rightarrow 0}x=0\]
Then e^0=1

Answer 3

Refresh to fix latex.

Answer 4

The part I don't quite understand is how does xln(1/x) = ln(1/x) / 1/x

Answer 5

Nvm I get it