Limits (intro) Knowledge-Based Practice

Math · Calculus · Math · Limits & Continuity

5 Math practice questions on Limits (intro). Questions that assess core concepts and understanding.

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Questions

1.
Let the function $f$ be defined by $f(x) = \begin{cases} 5 - x^2, & x < 2 \\ 3, & x = 2 \\ 2x - 3, & x > 2 \end{cases}$ . What is the value of $\lim_{x \to 2} f(x)$ ?
- A) 1
- B) 3
- C) 5
- D) The limit does not exist.
2.
What is the value of $\lim_{x \to 3^-} \frac{|x - 3|}{x - 3}$ ?
- A) 1
- B) 0
- C) -1
- D) -3
3.
What is the value of $\lim_{x \to 2} \frac{\frac{1}{x} - \frac{1}{2}}{x - 2}$ ?
- A) $\frac{1}{4}$
- B) $-\frac{1}{2}$
- C) 0
- D) $-\frac{1}{4}$
4.
What is the value of $\lim_{x \to 0} \frac{\sqrt{x + 9} - 3}{x}$ ?
- A) $\frac{1}{3}$
- B) $\frac{1}{6}$
- C) 0
- D) 6
5.
What is the value of $\lim_{x \to 3} \frac{x^2 - x - 6}{x - 3}$ ?
- A) 0
- B) 5
- C) 6
- D) Does not exist

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