Tìm giới hạn $\Large \underset{x\rightarrow 1}{lim}\dfrac{x^4-3x^2+2}{

Tìm giới hạn $\Large \underset{x\rightarrow 1}{lim}\dfrac{x^4-3x^2+2}{x^3+2x-3}$

• A.

  $\Large +\infty$.

• B.

  $\Large -\infty$.

• C.

  $\Large \dfrac{-2}{5}$.

• D.

  0.

Đáp án C

$\Large \underset{x\rightarrow 1}{lim}\dfrac{x^4-3x^2+2}{x^3+2x-3}$

$\Large =\underset{x\rightarrow 1}{lim}\dfrac{(x+1)(x-1)(x^2-2)}{(x-1)(x^2+x+3)}$

$\Large =\underset{x\rightarrow 1}{lim}\dfrac{(x+1)(x^2-2)}{(x^2+x+3)}$

$\Large =\dfrac{2(-1)}{5}=\dfrac{-2}{5}$.