Question

Alguém pode me ajudar com a letra (d) e (e)

Answer 1

d)
$\lim_{x \to 1} \frac{\frac{1}{x}-1}{x-1} = \lim_{x \to 1} \frac{\frac{1-x}{x}}{x-1} =\lim_{x \to 1} \frac{1-x}{x(x-1)} =\lim_{x \to 1} \frac{-1(x-1)}{x(x-1)} =$$\lim_{x \to 1} \frac{-1}{x}=\frac{-1}{1}=-1$

e)
$\lim_{x \to 0} \frac{\frac{1}{x-1}+\frac{1}{x+1}}{x}= \lim_{x \to 0} \frac{\frac{(x+1)+(x-1)}{x^{2}-1}}{x}=$$\lim_{x \to 0} \frac{(x+1)+(x-1)}{x(x^{2}-1)}=\lim_{x \to 0} \frac{2x}{x(x^{2}-1)}=\lim_{x \to 0} \frac{2}{x^{2}-1}=\frac{2}{-1}=-2$