Question

Show that f(x) = 2000x^4 and g(x) = 200x^4 grow at the same rate.

Answer 1

Answer:

The answer is "$f(x) \ and \ g(x)\text {are in same rate }$".

Explanation:

$\to f(x) = 2000x^4\\\\ \to g(x) = 200x^4$

$\to \lim_{n \to \infty} \frac{f(x)}{g(x)}=\frac{2000x^4 }{200x^4}=\frac{2000}{200}=10\\\\\to \lim_{n \to \infty} \frac{f(x)}{g(x)}= m\neq 10$

So,$f(x) \ and \ g(x)$ are in the same rate because M=10 is finite.