MTH 31
(16) Find the values a for which $\lim_{x\to a} f(x)$ exist. Explain using a graph.
$$f(x) = \begin{cases} 1 + \cos x & \text{if } x \le 0 \\ \sin x & \text{if } 0 < x \le \pi \\ \cos x & \text{if } x > \pi \end{cases}$$
(17) Find $\lim_{x\to 1} \frac{x^7 - 1}{x^{10} - 1}$.
(18) Find $\lim_{x\to 0} \frac{\sin 5x}{\sin 4x}$.
