Limits and Continuity

A student is trying to solve this problem $\lim_{x \to 0} \frac{\sin 5x}{x}$. Here is what this student did Step 1: $\lim_{x \to 0} \frac{\sin 5x}{x} \left( \frac{5}{5} \right)$ Step 2: $\lim_{x \to 0} \frac{5 \sin 5x}{5x}$ Step 3: $5 \cdot 1 = 5$ Is this student correct?

True or False: the limit of a constant a constant.

What type of discontinuity does $h(p)=\sqrt{\left|p\right|-4}/(\left|p\right|-4)$ exhibit as $p$ approaches $\pm 4$?

A pair of students are trying to solve this problem: $\lim_{x \to 0} \sec(2x)$. The following are the steps the students follow: Step 1: $\lim_{x \to 0} \sec(2x) = \lim_{x \to 0} \sec \cdot \lim_{x \to 0} (2x)$ Step 2 = $0 \cdot 0$ Step 3 = $0$ Are the students correct?

Find the limit of the function $f(x) = \frac{3x^2 - 4x + 2}{2x^2 - 5x + 3}$ as $x$ approaches 1.

Find the $\lim_{x \to 2} (5x^3 - 2x^2 + 4x - 1)$.

​​Consider the function $f(x) = \sqrt{x} + 2x$. Find the limit as $x$ approaches 4.

What is $\lim_{x \to -4} \frac{x^2 - x - 20}{x + 4}$?

Given that $\lim_{{x \to -\infty}} g(x) = L$ and $\lim_{{h \to 0}} \frac{g(-1+h)-g(-1)}{h} = m$, which expression accurately expresses L in terms of m?

When faced with computing $\lim_{{h \to 0}} \frac{(a+h)^n-a^n}{h}$ where $n$ is a positive integer, why would expansion using binomial theorem be less favorable than applying another technique?