Question

Find the value of the limit: $\underset{n\to \infty }{lim}\frac{1-2n^2}{5n^2-n+100}$

• A. $-1$
• B. $-\frac{2}{5}$
• C. $\frac{2}{5}$
• D. $1$
• E. No limit exists

Answer 1

Answer: (B)

$-\frac{2}{5}$

Given, $\underset{n\to \infty }{lim}\frac{1-2n^2}{5n^2-n+100}$

$\underset{n\to \infty }{lim}\frac{1-2n^2}{5n^2-n+100}=\frac{\frac{1}{n^2}-2}{5-\frac{1}{n}+\frac{100}{n^2}}$

When $n$ goes to infinite , we get $\frac{0-2}{5-0+0}=-\frac{2}{5}$