Matemática
alanalazari
3

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

+0
(1) Respostas
adineiamarinho

Resolução da questão, veja: Neste caso, é necessário que façamos a mudança dessa variável “x”, substituiremos “x” por “u²”, observe: [latex]\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}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}} [/latex] Espero que te ajude. '-'

Adicionar resposta