Evaluate the Given limit:


Evaluate the Given limit: $\lim _{x \rightarrow 3} \frac{x^{4}-81}{2 x^{2}-5 x-3}$


At $x=2$, the value of the given rational function takes the form $\frac{0}{0}$.

$\therefore \lim _{x \rightarrow 3} \frac{x^{4}-81}{2 x^{2}-5 x-3}=\lim _{x \rightarrow 3} \frac{(x-3)(x+3)\left(x^{2}+9\right)}{(x-3)(2 x+1)}$

$=\lim _{x \rightarrow 3} \frac{(x+3)\left(x^{2}+9\right)}{2 x+1}$


$=\frac{6 \times 18}{7}$



Leave a comment


Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now