Question

lim x-tende a 1
1- raiz de x
sobré 1-×^2

Answer 1

Resolução da questão, veja:

Neste caso, é necessário que façamos a mudança dessa variável “x”, substituiremos “x” por “u²”, observe:

$\mathtt{\displaystyle\lim_{x~\to~1}~\dfrac{1-\sqrt{x}}{1-x^{2}}}}}}}}~~\textsf{Fazendo~a~mudan\c{c}a~de~vari\'avel,~teremos}:}}}}}\\\\\\\\\\ \mathtt{\displaystyle\lim_{x~\to~1}~\dfrac{1-\sqrt{u^{2}}}{1-(u^{2})^{2}}}}}}}}\\\\\\\\\\ \mathtt{\displaystyle\lim_{x~\to~1}~\dfrac{1-|u|}{-u^{4}+1}}}}}}}}\\\\\\\\\\ \mathtt{\displaystyle\lim_{x~\to~1}~\dfrac{-u+1}{-u^{4}+1}}}}}}}\\\\\\\\\\\ \mathtt{\displaystyle\lim_{x~\to~1}~\dfrac{1}{u^{3}+u^{2}+u+1}}}}}}}}\\\\\\\\\\\ \mathtt{\displaystyle\lim_{x~\to~1}~\dfrac{1}{1^{3}+1^{2}+1+1}}}}}}}}\\\\\\\\\\\ \mathtt{\displaystyle\lim_{x~\to~1}~\dfrac{1}{1+1+1+1}}}}}}}}\\\\\\\\\\ \Large\boxed{\boxed{\boxed{\boxed{\boxed{\mathbf{~\therefore~\displaystyle\lim_{x~\to~1}~\dfrac{1-\sqrt{x}}{1-x^{2}}=\dfrac{1}{4}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}$

Espero que te ajude. '-'