Basic limit problems

$$\lim\limits_{x \to 3}\ x = 3.$$

$$\lim\limits_{x \to a} \ \left( x^2 + 7 \right) = a^2 + 7.$$

$$\begin{eqnarray} \lim\limits_{x \to \pi}\ \cos \left( \dfrac{x}{2} \right) &=& \cos \left( \dfrac{\pi}{2}\right) \\ \ &=& 1. \end{eqnarray}$$

$$\begin{eqnarray} \lim\limits_{x \to \infty}\ e^{-x} &=& \ e^{-\infty} \\ \ &=& 1. \end{eqnarray}$$

$$\lim\limits_{x \to a}\ \dfrac{x - 3}{x^2 + 7} = \ \dfrac{a- 3}{a^2 + 7}.$$

$$\begin{eqnarray} \lim\limits_{x \to \pi}\ x \cos x &=& \pi \cos \pi \\ \ &=& -\!\pi. \end{eqnarray}$$