Find the following limits: (a) $\lim _{x \rightarrow 0} \frac{\sin x}{x}$ (b) $\lim _{x \rightarrow 0}(1+x)^{1 / x}$ (c) $\lim _{x \rightarrow \infty} \frac{(1+x)^{\frac{x}{1+x}} \cos ^{4} x}{e^{x}}$

Carefully justify your answers.

[You may use standard results provided that they are clearly stated.]