Limit Laws Practice
About This MicroSim
Practice applying limit laws to evaluate limits algebraically. Problems range from basic single-rule applications to challenge problems requiring multiple limit laws.
Limit Laws Covered
| Law | Formula |
|---|---|
| Constant | \(\lim_{x \to c} k = k\) |
| Constant Multiple | \(\lim_{x \to c} [k \cdot f(x)] = k \cdot \lim_{x \to c} f(x)\) |
| Sum | \(\lim_{x \to c} [f + g] = \lim f + \lim g\) |
| Difference | \(\lim_{x \to c} [f - g] = \lim f - \lim g\) |
| Product | \(\lim_{x \to c} [f \cdot g] = \lim f \cdot \lim g\) |
| Quotient | \(\lim_{x \to c} \frac{f}{g} = \frac{\lim f}{\lim g}\) (if \(\lim g \neq 0\)) |
| Power | \(\lim_{x \to c} [f]^n = [\lim f]^n\) |
How to Use
- Select Difficulty: Choose Basic, Intermediate, or Challenge
- Read the Problem: See the limit expression to evaluate
- Type Your Answer: Use keyboard to enter the numerical result
- Check Answer: Get immediate feedback on your answer
- Show Solution: View the step-by-step solution
Difficulty Levels
- Basic: Single limit law (e.g., \(\lim_{x \to 3} 5x\))
- Intermediate: Two laws combined (e.g., \(\lim_{x \to 2} (x^2 + 3x)\))
- Challenge: Three or more laws including quotients
Lesson Plan
Learning Objectives
After using this MicroSim, students will be able to:
- Apply limit laws to evaluate algebraic limits
- Select the appropriate limit law for each term
- Calculate limits of polynomial and rational expressions
Suggested Activities
- Speed Drill: See how many basic problems you can solve in 3 minutes
- Explain Your Reasoning: For each problem, verbally state which law(s) you used
- Create Similar Problems: Write your own limit problems for a partner
Assessment Questions
- Find \(\lim_{x \to 4} (2x^2 - 3x + 1)\)
- Find \(\lim_{x \to 2} \frac{x^2 + 1}{x - 3}\)
- Which limit law would you use first for \(\lim_{x \to 1} (x + 2)(x - 3)\)?
Embedding
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