l`hopitals regel

[Integralen]

A)
[tex]lim_{x\rightarrow 0^{+}} \: \: x^{\frac{a}{b}} lnx=[/tex]

B)
[tex]lim_{x\rightarrow 0^{+}} \: \: \frac{lnx}{x^{-\frac{a}{b}}}=[/tex]

C)
[tex]lim_{x\rightarrow 0^{+}} \: \: \frac{\frac{1}{x}}{- \frac{a}{b}x^{- \frac{a}{b}-1}}=[/tex]

D)
[tex]lim_{x\rightarrow 0^{+}} \: \: - \frac{b}{a} x^{\frac{a}{b}}=[/tex]

Hvordan ble C til lik D ?

[claudius]

[tex]-\frac{b}{a}x^{-1}\cdot x^{\frac{a}{b}+1}=-\frac{b}{a}x^{\frac{a}{b}}\\ \frac{1}{x^{-\frac{a}{b}}}=x^{\frac{a}{b}},\; \frac{1}{\frac{a}{b}} = \frac{b}{a}[/tex]

[Integralen]