Question

Find the limits of the following expression $\frac{(3-x)(x+5)(2-7x)}{(7x-1)(x+1{)}^3}$, $\left(1\right)$ when $x=\infty$, $\left(2\right)$ when $x=0$.

Answer 1

(1) When $x\to \infty$

Dividing numerator and denominator of the given exprssion with $x^4$, We get:

$\underset{x\to \infty }{lim}\frac{1/x(3/x-1)(1+5/x)(2/x-7)}{(7-1/x)(1+1/x)}=\frac{0\times -1\times 1\times -7}{7\times 1}=0$

(2) When $x=0$ expression will become

$\frac{3\times 5\times 2}{-1\times 1}=-30$