Question

Evaluate $\underset{x\to 0^{-}}{lim}\frac{x^2-3x+2}{x^3-2x^2}$.

• A. $\infty$
• B. 0
• C. 1
• D. $-\infty$

Answer 1

The correct option is D $-\infty$

$L=\underset{h\to 0}{lim}\frac{(-h{)}^2-3(-h)+2}{(-h{)}^3-2(-h{)}^2}$

$=-\underset{h\to 0}{lim}\frac{h^2+3h+2}{h^3+2h^2}$

For $h\to 0$, numerator $\to$ 2 and denominator $\to$ 0.

Therefore, $L\to -\infty$