The uploaded image contains a set of mathematical problems, primarily involving calculus concepts like limits and continuity, as well as some function analysis. I'll help break down and solve each of these problems step-by-step. Here is a brief look at some of the problems:

Section Overview

The problems are divided into two main sections:

1. True/False or Fill-in-the-Blanks — focusing on continuity, natural domains, and properties of limits and functions.
2. Limit Calculations — requiring detailed computation of limits using limit laws and possibly L'Hôpital's rule for indeterminate forms.

Let's start analyzing the problems individually. I'll proceed with solutions for each part unless you'd prefer a focus on specific questions.

Would you like a full solution for each problem, or are you looking for help on specific items?

Relative Questions for Further Exploration

1. How can we identify and determine the natural domain of a function?
2. What conditions must be met for a function to be continuous at a point?
3. How can we use L'Hôpital's Rule effectively when computing limits?
4. What are the steps to find the range of a composite function?
5. How does one approach limits that result in indeterminate forms like $0/0$ or $\infty/\infty$?

Tip

When dealing with limits at a point where direct substitution leads to an indeterminate form, consider factoring, rationalizing, or applying L'Hôpital's Rule to simplify the expression.