Question

The value of $\underset{y\to 7}{lim}\frac{y^2-4y-21}{3y^2-17y-28}$ is

• A. $\frac{-2}{5}$
• B. $\frac{2}{5}$
• C. Limit doesn't exist
• D. $0$

Answer 1

The correct option is B $\frac{2}{5}$

$\underset{y\to 7}{lim}\frac{y^2-4y-21}{3y^2-17y-28}=\underset{y\to 7}{lim}\frac{(y-7)(y+3)}{(y-7)(3y+4)}$
This is $\frac{0}{0}$ form
$=\underset{y\to 7}{lim}\frac{(y+3)}{(3y+4)}=\frac{10}{25}=\frac{2}{5}$