What a Limit Says

Where the function is heading, not where it lands.

11 problems · about 24 minutes · AP Calculus AB 1.2, 1.3

NameDate

Figure — use these to answer the problems

Approach the asymptote from either side and watch the outputs run away.

y = 1/x + 0

x approaches2

Figure 1

Straightforward practice. Get the method working first.

4 problems

Limit of (x² − 16)/(x − 4) as x approaches 4?
Answer
Limit of 3x + 1 as x approaches 2?
Answer
Limit of (x² − 1)/(x − 1) as x approaches 1?
Answer
Left limit is 4, right limit is 4. Does the limit exist? 1 for yes, 0 for no.
Answer

The same ideas with more to keep track of.

3 problems

Left limit is 2, right limit is 5. Does the limit exist? 1 for yes, 0 for no.
Answer
6
Select every statement that is true about limits.
- A limit can exist where the function is undefined.
- The limit always equals the value at the point.
- Both one-sided limits must agree.
- 0/0 means the limit is zero.
- Tick every box that applies.
Limit of 5 as x approaches 100?
Answer

Mixed problems. Work out what kind of question it is before you start.

4 problems

Limit of (x² − 25)/(x − 5) as x approaches 5?
Answer
9
Order these steps for a limit that gives 0/0 on substitution.
Write 1 to 4 in the boxes to put these in order.
- Substitute and get 0/0
- Factor the numerator and denominator
- Cancel the shared factor
- Substitute again
The Removable Discontinuity
What is the limit of (x² − 9)/(x − 3) as x approaches 3?
Answer
Value Against Limit
f(2) = 10 but the outputs near 2 approach 3. What is the limit as x approaches 2?
Answer