Question

Se considera functia f:(2, infinit) -> R, f (x)= x-1 supra x-2 .
a) Calculați lim f (x) x->3
b) calculați lim f (x) supra x ; x-> infinit

Answer 1

a)[tex] \lim_{x \to 3}f(x)= \lim_{x \to 3} \frac{x-1}{x-2}= \frac{3-1}{3-2}=2 [/tex]
b)$\lim_{x \to \infty} \frac{f(x)}{x}= \lim_{x \to \infty} \frac{x-1}{x(x-2)} =\lim_{x \to \infty} \frac{x(1- \frac{1}{x}) }{x(x-2)} =\lim_{x \to \infty} \frac{1- \frac{1}{x} }{x-2}=$1/∞=0