Unit 1: Limits & Continuity
Calculus AB · Unit 1 · Paper 2

Limits & Continuity unit test

A test on this unit alone, marked as a percentage and a letter grade — for the test your class is actually sitting, rather than for May. Answer everything, then submit once: seeing the answer to question 3 before attempting question 4 makes the final percentage meaningless.

Paper 1Paper 2Paper 3
Each paper is built from this unit’s 19 terms and is the same for everyone, so a teacher can assign “Unit 1, Paper 2” and every student sits the identical test. Multiple choice is marked objectively; the written sections you mark yourself against the model answer and rubric.
Suggested time 36 min 33 points0/17 attempted
1

Evaluating a limit algebraically

2

Limits at infinity of rational functions

3

Continuity on an interval

4

Limit of a piecewise function at a boundary

5

Indeterminate form 0/0

6

Vertical asymptote

7

Special trig limits

8

One-sided limits

9

Horizontal asymptote

10

Extreme Value Theorem

11

Showing a limit does not exist

12

Infinite limit vs limit at infinity

Short answer 1. Define or explain: Squeeze theorem

3 pts

Short answer 2. Define or explain: Removable discontinuity

3 pts

Short answer 3. Define or explain: Intermediate Value Theorem

3 pts

Short answer 4. Define or explain: Continuity of piecewise functions

3 pts

Free response

9 pts

This course has no free-response prompt tagged to this unit, so one from elsewhere in the course is used. It is still worth writing — the skill transfers.

Consider the differential equation dy/dx = xy², and let y = f(x) be the particular solution with f(0) = 1.

Write an equation for the line tangent to the graph of f at (0, 1), and use it to approximate f(0.5).

Use separation of variables to find the particular solution y = f(x).

State the largest open interval containing x = 0 on which the solution from part (b) is defined, and explain what limits it.