Question

Find the value of
a.) lim (x²-1)/(x²+1)
x−>∞
​

Answer 1

Answer:

$\displaystyle\lim_{x \to \infty} \frac{x^2-1}{x^2+1} \\ \text{take x^2 common from numerator and denominator} \\ \displaystyle\lim_{x \to \infty} \dfrac{1-\frac{1}{x^2}}{1+\frac{1}{x^2}} \\

\text{Now put the limit}

\\

\displaystyle\lim_{x \to \infty} \frac{1-0}{1+0}= 1

$