← Back to Evaluating Limits Analytically

Evaluating Limits Analytically - Worksheet 2 - 12th Grade

Easy

Evaluate limits with the approach direction stated and distinguish limits from function values.

easy: Start with the preview and follow the worked example.

18 problems · 25-30 minutes · Skills: limits, calculus, algebra

About This Worksheet

This easy-level worksheet contains 18 problems designed for 12th Grade students practicing evaluating limits analytically. Easy worksheets use simpler numbers and straightforward problem types to build confidence and reinforce foundational skills.

Manipulate algebraic expressions and understand functions, limits and derivative notation.

  • Evaluate limits with the approach direction stated and distinguish limits from function values.
  • Check your result using the method in the example before moving to the next question.

How to Solve: Worked Example

Example Problem: Find lim as x → 4 of (x² − 16)/(x − 4).
Solution Steps:
  1. Factor the numerator as (x − a)(x + a).
  2. For x near but not equal to a, cancel the common factor.
  3. Evaluate x + 4 at x = 4.
Answer: 8
Tip: Check your result using the method in the example before moving to the next question.
1
Find lim as x → 2 of (x² − 4)/(x − 2).
2
Find lim as x → 6 of (x² − 36)/(x − 6).
3
Find lim as x → 5 of (x² − 25)/(x − 5).
4
Find lim as x → 4 of (x² − 16)/(x − 4).
5
Find lim as x → 8 of (x² − 64)/(x − 8).
6
Find lim as x → 3 of (x² − 9)/(x − 3).
7
Find lim as x → 7 of (x² − 49)/(x − 7).
8
Find lim as x → 1 of (x² − 1)/(x − 1).
9
Find lim as x → 2 of (x² − 4)/(x − 2).
10
Find lim as x → 7 of (x² − 49)/(x − 7).
11
Find lim as x → 8 of (x² − 64)/(x − 8).
12
Find lim as x → 5 of (x² − 25)/(x − 5).
13
Find lim as x → 6 of (x² − 36)/(x − 6).
14
Find lim as x → 3 of (x² − 9)/(x − 3).
15
Find lim as x → 6 of (x² − 36)/(x − 6).
16
Find lim as x → 2 of (x² − 4)/(x − 2).
17
Find lim as x → 6 of (x² − 36)/(x − 6).
18
Find lim as x → 1 of (x² − 1)/(x − 1).

Answer Key

1. 42. 123. 104. 85. 166. 67. 148. 29. 410. 1411. 1612. 1013. 1214. 615. 1216. 417. 1218. 2

Practice next

Report a question or answer error

Frequently Asked Questions

How do I download this evaluating limits analytically - worksheet 2 worksheet?

Click "Download PDF" for a file, or "Print" to use your browser. You can save it as a PDF or print it directly. The answer key will be on a separate page.

How do I find worksheets at different difficulty levels?

Each subtopic has 10 worksheets: Worksheets 1-3 are Easy, 4-7 are Medium, and 8-10 are Hard. Start with Easy worksheets to build confidence, then progress to harder ones.

What skills does this limits & continuity worksheet cover?

This worksheet focuses on limits, calculus, algebra. It is designed for 12th Grade students and provides structured practice through varied problem types with a worked example to guide students before they begin.

Can I use this worksheet in my classroom?

Yes. All worksheets on K12Worksheets are free for classroom use. You can print copies for your entire class. With 10 worksheets per subtopic at three difficulty levels, you have plenty of options for differentiated instruction and individualized practice.

How many problems are on this worksheet?

This worksheet contains 18 problems. It typically takes 25-30 minutes to complete. An answer key with all solutions is included so parents and teachers can check work quickly.