Question

If $f\left(x\right)=\{\begin{array}{cc}7-4x,& x<1\\ x^2+2,& x\ge 1\end{array}$
then value of $\underset{x\to -6}{lim}f\left(x\right)$ is

• A. $14$
• B. $31$
• C. it does not exist
• D. $18$

Answer 1

The correct option is B $31$

$\because -6<1$
So, there will be values of $x$ on both sides of $-6$ in the range $x<1$ and so we can assume that, in the limit we will have $x<1$. This will allow us to use piece of the function in that range and then just use standard limit technique to compute the limit.
$\underset{x\to -6}{lim}f\left(x\right)=\underset{x\to -6}{lim}(7-4x)=31$