Answer
If $mn$, then we only get $x$ in the denominator.
Thus as $x$ increases, then the quotient will decrease.
That gives, $\lim_\limits{x\to +\infty}\dfrac{c_nx^n}{d_mx^m}=0$
Work Step by Step
Since, we know that the end behavior of a rational function matches the end behavior of the quotient of the highest degree term in the numerator divided by the highest degree term in the denominator.
Simplify $\lim_\limits{x\to +\infty}\dfrac{c_0+c_1x+...+c_nx^n}{d_0+d_1x+...+d_mx^m}$
We get, $\lim_\limits{x\to +\infty}\dfrac{c_nx^n}{d_mx^m}$
Now, there can be three cases $m n$.
If $mn$, then we only get $x$ in the denominator.
Thus as $x$ increases, then the quotient will decrease.
That gives, $\lim_\limits{x\to +\infty}\dfrac{c_nx^n}{d_mx^m}=0$
