This ap calculus limits quiz asks 10 multiple-choice questions on limits and continuity, and each answer comes with a short explanation.
This 10-question multiple choice quiz checks limits from graphs, algebraic limits, limits at infinity, continuity and the Intermediate Value Theorem. Pick the one correct answer for each question, then read the explanation to learn from any miss.
AP Calculus ABCommon Core: AP Calculus AB Unit 1
🎯 Limits and Continuity – AP Calculus AB math quiz
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Question 1
Use the graph of \(g\) to find \(\lim_{x\to 4} g(x)\).Graph for question 1.
The graph of a function is shown. What kind of discontinuity occurs at \(x=2\)?Graph for question 4.
ARemovable
BJump
CInfinite
DThere is no discontinuity
Question 5
Evaluate \(\lim_{x\to 0} \frac{\sin 3x}{x}\).
A\(1\)
B\(3\)
C\(0\)
D\(\frac{1}{3}\)
Question 6
Let \(f(x)=kx+2\) when \(x\le 2\) and \(f(x)=x^{2}+k\) when \(x > 2\). For what value of \(k\) is \(f\) continuous at \(x=2\)?
A\(k=1\)
B\(k=0\)
C\(k=4\)
D\(k=2\)
Question 7
A function \(f\) is continuous on \([2,6]\) with \(f(2)=4\) and \(f(6)=-8\). Which statement must be true?
A\(f(c)=-11\) for some \(c\) in \((2,6)\)
B\(f\) is decreasing on \([2,6]\)
C\(f(c)=0\) for exactly one \(c\) in \((2,6)\)
D\(f(c)=-1\) for some \(c\) in \((2,6)\)
Question 8
Which line is a horizontal asymptote of \(f(x)=\frac{3x^{2}+1}{x^{2}-4}\)?
A\(y=3\)
B\(y=0\)
C\(x=2\)
D\(y=-\frac{1}{4}\)
Question 9
The graph of \(f\) is shown. What is \(\lim_{x\to 1} f(x)\)?Graph for question 9.
A\(2\)
B\(4\)
CThe limit does not exist
D\(3\)
Question 10
Which function has a removable discontinuity at \(x=3\)?
A\(\frac{1}{x-3}\)
B\(\frac{x^{2}-9}{x-3}\)
C\(\frac{|x-3|}{x-3}\)
D\(\frac{x}{x^{2}+3}\)
🎉 Quiz complete!
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How does this quiz work?
Read each question, choose one answer among A, B, C and D, then check it: a short explanation appears after every answer. Your score out of 10 is shown at the end, and you can restart the quiz as often as you like.
What should you review before the quiz?
Reread the key facts of the lesson and the worked example. If a question is hard, go back to the matching part of the lesson, then try the quiz again. Write your work on scrap paper: most mistakes come from skipping a step, not from the idea itself.
Remember:
AP Calculus AB Unit 1: \(\lim_{x\to a} f(x)=L\) means \(f(x)\) gets arbitrarily close to \(L\) as \(x\) gets close to \(a\), from both sides.
The two-sided limit exists only when \(\lim_{x\to a^{-}} f(x)=\lim_{x\to a^{+}} f(x)\).
Continuity at \(x=a\) needs three things: \(f(a)\) is defined, \(\lim_{x\to a} f(x)\) exists, and the two are equal.
Discontinuities come in three kinds: removable (hole), jump, and infinite (vertical asymptote).
The Intermediate Value Theorem: if \(f\) is continuous on \([a,b]\) and \(k\) lies between \(f(a)\) and \(f(b)\), then \(f(c)=k\) for some \(c\) in \((a,b)\).
How to use this ap calculus limits quiz
Retake this ap calculus limits quiz until every answer is right, then move on to the worksheet and the test.
