Question

Alguém saber o resultado?

Answer 1

Derive numerador e denominador e aplique o limite se possivel

$\displaystyle \lim_{x \to 1} \dfrac{x^3-3x^2+5x-3}{x^2+x-2} \quad \mbox{derivando}\\\\\displaystyle \lim_{x \to 1} \dfrac{3x^{3-1}-3\cdot2x^{2-1}+5\cdot 1 x^{1-1}-0}{2x^{2-1}+1x^{1-1}-0}\\\\\displaystyle \lim_{x \to 1} \dfrac{3x^2-6x+5}{2x+1}\quad\mbox{aplicando o limite}\\\\\displaystyle \lim_{x \to 1} \dfrac{3x^2-6x+5}{2x+1}=\dfrac{3(1)^2-6(1)+5}{2(1)+1}=\dfrac{2}{3}$