Question

Limite de X ---> -1

$\sqrt{2x² +3x-3 /5x-4 }$

Answer 1

Olá



Basta substituir o valor de 'x', já que esse limite não se trata de uma indeterminação.



$\displaystyle\mathsf{ \lim_{x \to -1} ~ \sqrt{ \frac{2x^2+3x-3}{5x-4} } }\\\\\\\\\\\mathsf{ \lim_{x \to -1} ~ \sqrt{ \frac{2(-1)^2+3(-1)-3}{5(-1)-4} } }\\\\\\\\\\\mathsf{ \lim_{x \to -1} ~ \sqrt{ \frac{2-3-3}{-5-4} } }\\\\\\\\\\\mathsf{ \lim_{x \to -1} ~ \sqrt{ \frac{-4}{-9} } }\\\\\\\\\\\mathsf{ \lim_{x \to -1} ~ \sqrt{ \frac{4}{9} } }$


$\displaystyle \mathsf{ \lim_{x \to -1} ~ \frac{ \sqrt{4} }{ \sqrt{9} } ~=~ \frac{2}{3} }\\\\\\\\\\\boxed{\mathsf{ \lim_{x \to -1} ~ \sqrt{ \frac{2x^2+3x-3}{5x-4} }~=~ \frac{2}{3} }}$





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