Unit 1: Limits & Continuity
Calculus AB · Unit 1 · Paper 3

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 3” 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

Special trig limits

2

Horizontal asymptote

3

One-sided limits

4

Limit of a piecewise function at a boundary

5

Infinite limit vs limit at infinity

6

Squeeze theorem

7

Limit definition informally

8

Intermediate Value Theorem

9

Continuity of piecewise functions

10

Removable discontinuity

11

Showing a limit does not exist

12

Evaluating a limit algebraically

Short answer 1. Define or explain: Extreme Value Theorem

3 pts

Short answer 2. Define or explain: Three conditions for continuity at a

3 pts

Short answer 3. Define or explain: Continuity on an interval

3 pts

Short answer 4. Define or explain: Limits involving absolute value

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.