Question

LIMITES

Lim √h-1 / h-1 com h tendendo a 1.

Answer 1

$\lim_{h \to \ 1 \frac{ \sqrt{h}-1 }{h-1}$=$\frac{ \sqrt{1}-1 }{1-1} = \frac{0}{0}(SI)$

$\lim_{h \to \ 1 \frac{ \sqrt{h}-1 }{h-1} . \frac{( \sqrt{h}+1 )}{( \sqrt{h} +1)}$

$(a-b)(a+b)=a^2-b^2$
$( \sqrt{h}-1)( \sqrt{h}+1)= (\sqrt{h})^2-1^2$
$( \sqrt{h}-1)( \sqrt{h}+1)= h-1$

$\lim_{h \to \ 1 \frac{(h-1)}{(h-1)( \sqrt{h}+1) }$
$\lim_{h \to \ 1 \frac{1}{ \sqrt{h} +1} = \frac{1}{ \sqrt{1+1} }$=$\frac{1}{2}$