oblicz granice

[olciaa]

\(\lim_{x\to0^+} \sqrt{x}lnx\)
\(\lim_{x\to \infty } \frac{lnx}{ \sqrt{x^2-1} }\)

[radagast]

\(\lim_{x\to0^+} \sqrt{x}lnx=\lim_{x\to0^+} \frac{lnx}{ \frac{1}{\sqrt{x}} } =\lim_{x\to0^+} \frac{lnx}{x^{-\frac{1}{2} } }=^H\lim_{x\to0^+} \frac{ \frac{1}{x} }{-\frac{1}{2}x^{-\frac{3}{2} } }=\lim_{x\to0^+} -2 \sqrt{x} = 0\)

[radagast]

\(\lim_{x\to \infty } \frac{lnx}{ \sqrt{x^2-1} }=^H \lim_{x\to \infty } \frac{ \frac{1}{x} }{ \frac{2x}{2\sqrt{x^2-1} } }=\lim_{x\to \infty } \frac{\sqrt{x^2-1}}{x^2} =0\)