Question

Solve $\underset{x\to a}{lim}\frac{x^2-(a+1)x+a}{x^3-a^3}$

• A. $\frac{a-2}{a^2}$
• B. $\frac{a-1}{3a^2}$
• C. $\frac{a+1}{3a^2}$
• D. None of these

Answer 1

Answer: (B)

$\frac{a-1}{3a^2}$

$\underset{x\to a}{lim}\frac{x^2-(a+1)x+a}{x^3-a^3}=\underset{x\to a}{lim}\frac{f\left(x\right)}{g\left(x\right)}$

$f\left(a\right)=0+g\left(a\right)=0$

so : $\frac{0}{0}$ from by L-Hopital rule.

$\underset{x\to a}{lim}\frac{2x-(a+1)}{3x^2}=\frac{2a-a-1}{3a^2}=\frac{a-1}{3a^2}$