Solution
= Solution
For $x>0$, the exponent $x/(1+x)$ lies in $(0,1)$, and $0\leq\cos^4x\leq1$. Consequently
$$
0\leq\frac{(1+x)^{x/(1+x)}\cos^4x}{e^x}\leq\frac{1+x}{e^x}\leq\frac{2(1+x)}{x^2}.
$$
The last inequality uses the positive-term <power series> $e^x=\sum_{k\geq0}x^k/k!\geq x^2/2$ for $x>0$. The final bound tends to zero, so the <squeeze theorem> gives \b[limit $0$].