Let's analyze the uploaded mathematical problem. It consists of two sections:

Section 1: Continuity Analysis

1. Determine the continuity of the functions and identify the types of discontinuities. Then, plot the graphs:
   • (a) $y = \frac{x^2 + 1}{x + 2}$
   • (b) ( y = \begin{cases} (x-1)^3 & \text{if } x \leq 2, \ 1 & \text{if } 2 < x \leq 3, \ 3x - 8 & \text{if } x > 3 \end{cases} )

Section 2: Limit Computations

1. Compute the following limits:
   • (a) $\lim_{x \to -2} \frac{x^3 + 4x^2 + 7x + 6}{x^2 + x - 2}$
   • (b) $\lim_{x \to +\infty} (x^2 + 5 - \sqrt{x^2 + 7})x$
   • (c) $\lim_{x \to +\infty} \frac{4x + 1}{4x - 5}$
   • (d) $\lim_{x \to 0} \frac{1 - \cos^3(2x)}{7x^2}$
   • (e) $\lim_{x \to \pi} \frac{1 - \sin(x/2)}{\pi - x}$
   • (f) $\lim_{x \to 1} \frac{\sqrt[3]{1 + \ln^2 x - 1}}{1 + \cos(\pi x)}$

Would you like me to solve Section 1, Section 2, or both? Please let me know if you'd prefer detailed step-by-step explanations for each problem!