Límites Ejercicio Resuelto 6
Calcular:
a) {\lim_{x\rightarrow{}0}\frac{tg(Mx)-Mx}{2x^{2}·tg(Mx)}}
b) {\lim_{x\rightarrow{}0}\frac{Ln[sin(mx)]}{Ln[sin(x)]} con m>0}
c) {\lim_{x\rightarrow{}∞}\frac{2^{x+2}+3^{x+2}}{2^{x}+3^{x}}}
d) {\lim_{x\rightarrow{}0}\frac{tg x-sin x}{x-sinx}}
e) {\lim_{x\rightarrow{}0}\frac{tg (x)}{tg (5x)}}
f) {\lim_{x\rightarrow{}0}\frac{x·arctg (\frac{x}{2})}{cos x·sin^{2} (2x)}}
g) {\lim_{x\rightarrow{}∞}[x-x^{2}·Ln(1+\frac{1}{x})]}
h) {\lim_{x\rightarrow{}0}[(\frac{1}{x})^{2}-\frac{cotg x}{x}]}
i) {\lim_{x\rightarrow{}0}(\frac{a^{x}-b^{x}}{c^{x}-d^{x}}) con a,b,c,d>0}
j) {\lim_{x\rightarrow{}∞}x·(\sqrt[3] {1+\frac{a}{x}}-1)}
k) {\lim_{x\rightarrow{}1}(\frac{x}{x-1}-\frac{1}{Ln(x)})}
l) {\lim_{x\rightarrow{}3}\frac{1}{3x-9}·(\frac{5}{4x-2}-\frac{2}{x+1})}
m) {\lim_{x\rightarrow{}∞}\frac{(x^{2}+1)·sin (\frac{\pi}{x})}{x}}
n) {\lim_{x\rightarrow{}0^{+}}x^{x}}
o) {\lim_{x\rightarrow{}0}[cos(x)]^{cotg^{2}x}}
p) {\lim_{x\rightarrow{}∞}[\frac{x+2}{2x^{2}-5}]^{\frac{x-2}{x^{2}+6}}}
q) {\lim_{x\rightarrow{}0^{+}}[cotg x]^{sin x}}
r) {\lim_{x\rightarrow{}1/2^{+}}(2x^{2}+3x-2)^{tg(\pi·x)}}
