Precalculus Introduction to Limits Quiz: 10 Questions with Explanations

Precalculus math quiz: Introduction to Limits – Maths PDF

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This limits quiz for Precalculus covers introduction to limits (Common Core F-IF.B.6, F-IF.C.7d), with a free PDF to print.

Pick the best answer for 10 questions on limits and continuity. Explanations name common mistakes, such as thinking a hole means the limit does not exist.

Precalculus · Common Core State Standards: F-IF.B.6, F-IF.C.7d

Limits quiz: 10 questions

Question 1

What is the average rate of change of \(f(x)=x^{2}\) from \(0\) to \(4\)?

Question 2

Evaluate \(\lim_{x\to3}(2x+5)\).

Question 3

Evaluate \(\lim_{x\to2}\frac{x^{2}-4}{x-2}\).

Question 4

The graph shows a hole. What is the limit as \(x\to2\)?

Graph with a hole.

Question 5

Evaluate \(\lim_{x\to\infty}\frac{5x^{2}+1}{2x^{2}-7}\), which is the height of the horizontal asymptote.

Graph with a horizontal asymptote.

Question 6

The graph shows a jump at \(x=2\). What can you say about \(\lim_{x\to2}f(x)\)?

Left limit 3 and right limit 4.

Question 7

For \(f(x)=x^{2}\), the average rate of change on \([2,2+h]\) is…

Question 8

Which describes a removable discontinuity?

Question 9

As \(x\to\infty\), the concentration \(C(t)=\frac{5t}{t+2}\) approaches…

Question 10

What does \(\lim_{x\to a^{+}}f(x)\) mean?

Remember

Average rate of change: (f(b) – f(a))/(b – a), the secant slope.
lim x to a of f(x) = L means f(x) approaches L as x approaches a from both sides.
The limit can exist even if f(a) is undefined (a hole).
Two-sided limit exists only if the left and right limits are equal.
f is continuous at a if f(a) exists, the limit exists and they are equal.

How to use this limits quiz

Answer each question, read the explanation that appears, and keep track of your score. A score of 8 out of 10 or more means you are ready for the test.

Download the limits quiz as a PDF with the button below and keep it with your notes.

All Precalculus chapters: Precalculus math.

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