Question

lim (3x^2+4/ 5x^4+ 7x^2+1)

x→∞

Answer 1

We have given the limit

$limx\rightarrow \infty \dfrac{3x^2+4}{5x^4+ 7x^2+1}$

$limx\rightarrow \infty \dfrac{x^2(3+\dfrac{4}{x^2})}{x^4(5+\dfrac{7}{x^2}+\dfrac{1}{x^4})}$

$limx\rightarrow \infty \dfrac{(3+\dfrac{4}{x^2})}{(5+\dfrac{7}{x^2}+\dfrac{1}{x^4})}$

After putting the limit we get 0.

Hence, $limx\rightarrow \infty \dfrac{3x^2+4}{5x^4+ 7x^2+1} = 0$