Question

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

• A. $2$
• B. $5$
• C. $3$
• D. $-1$

Answer 1

Answer: (B)

$\underset{x\to 1}{\lim }$$\frac{\left(x-1\right)\left(x^2+2x+2\right)}{sin\left(x-1\right)}$
$=\underset{x\to 1}{\lim }$$\frac{x-1}{sin\left(x-1\right)}\underset{x\to 1}{\lim }$$\left(x^2+2x+2\right)$
$=1\left(1+2+2\right)=5$.