+Kilka trudniejszych granic

[profesorq]

Obliczyć granice

a) \(\displaystyle{ \lim_{x \to 1} (\frac{1}{lnx}-\frac{1}{x-1})}\)
b) \(\displaystyle{ \lim_{x \to 0} (\frac{3^x + 5^x}{2})^{\frac{1}{x}}}\)
c) \(\displaystyle{ \lim_{x \to 0} \frac{(2+x)^x - 2^x}{x^2}}\)
d) \(\displaystyle{ \lim_{x \to + } \frac{x-sinx}{x+cosx}}\)
e) \(\displaystyle{ \lim_{x \to + } [x^2(arctgx-\frac{\pi}{2})+x]}\)

[Lorek]

d) z tw. o 3 funkcjach =1

[profesorq]

jak to udowodnić ?

[Lady Tilly]

Obliczyć granice
a) \(\displaystyle{ \lim_{x \to 1} (\frac{1}{lnx}-\frac{1}{x-1})}\)

\(\displaystyle{ \lim_{x \to 1} (\frac{1}{lnx}-\frac{1}{x-1})=\frac{1}{2}}\)