Limit of Fraction $$\lim_{x \to \infty} \frac{(1 + x)^{x/(1 + x)}\cos^{4}x}{e^{x}}$$
Attempt: I've tried evaluating the limits of the terms individually using the property of limits. Also, $y=1/x$ subsituition hasn't helped me, any help will be appreciated. 

Hint: For positive $x$, the top is $\ge 0$ and $\le 1+x$.
Now use Squeezing. 
