Unit Test 1: Limits

$$f(x)$$

$$x$$

According to this graph, what is $\lim_{x \to 0} f(x)$?

A) $0$ B) $1$ C) $2$ D) Does not exist

According to this graph, which statement is true?

A) $f(0) = 2$ B) $f(0) = 0$ and $\lim_{x \to 0} f(x) = 2$ C) $f(0) = 2$ and $\lim_{x \to 0} f(x) = 2$ D) The limit does not exist

$\lim_{x \to 2} f(x) = 5, \lim_{x \to 2} g(x) = 3$. Find $\lim_{x \to 2} [2f(x)-g(x)]$

A) $7$ B) $8$ C) $10$ D) $13$

Evaluate: $\lim_{x \to 0} \frac{\sin x}{x}$

A) $1$ B) $0$ C) $\infty$ D) Does not exist

Evaluate: $\lim_{x \to 3} (2x^2 - 5)$

A) $7$ B) $18$ C) $13$ D) $10$

Evaluate: $\lim_{x \to 4} \frac{x^2-16}{x-4}$

A) $7$ B) $8$ C) $10$ D) $13$

Evaluate the infinite limit: $\lim_{x \to \infty} \frac{5x^2+1}{2x^2-3}$

A) $\frac{5}{2}$ B) $0$ C) $\infty$ D) $-\frac{1}{3}$

Evaluate: $\lim_{x \to 2}\frac{x^2-4}{x-2}$

A) $2$ B) $4$ C) $6$ D) Does not exist

Given: $$ f(x)= \begin{cases} x+3, & x>1,\\ 2x, & x \le 1, \end{cases} $$ What is $\lim_{x\to1}f(x)$?

A) $2$ B) $3$ C) $4$ D) Does not exist

Evaluate: $\lim_{x \to 0}\frac{\sqrt{x+4}-2}{x}$

A) $\frac{1}{2}$ B) $\frac{1}{4}$ C) $1$ D) $0$