lim-x-3x-2-5-x-

Question Number 116859 by Study last updated on 07/Oct/20

l i \underset{x \to \infty}{m} \frac{3 x^{2}}{5^{x}} = ?

Commented by JDamian last updated on 07/Oct/20

As exponential function increases more rapidly than parabola, you even can get this limit intuitively

Answered by bemath last updated on 07/Oct/20

\lim_{x \to \infty} \frac{6 x}{5^{x} . \ln (5)} = \lim_{x \to \infty} \frac{6}{5^{x} . {(\ln (5))}^{2}} = 0

Commented by bemath last updated on 07/Oct/20

Answered by 1549442205PVT last updated on 07/Oct/20

l i \underset{x \to \infty}{m} \frac{3 x^{2}}{5^{x}} = This is the form \frac{\infty}{\infty} . Hence,

using L^{'} Hopital rule we have

I = l i \underset{x \to \infty}{m} \frac{3 x^{2}}{5^{x}} = \lim_{x \to \infty} \frac{6 x}{5^{x} \ln 5} = \lim_{x \to \infty} \frac{6}{5^{x} {(\ln 5)}^{2}}

= 0