Calculus I · Limits and Continuity · review
Common Limits Exam Errors
Review Common Limits Exam Errors with a concise concept summary, common errors, and links to targeted practice.
Where this chapter fits
Chapter 7: Synthesis
Bring the unit together by choosing methods, explaining decisions, and correcting weak spots before an exam.
Reading lens: Can you diagnose the limit type and justify a method before beginning the algebra? Keep that question in view while reading Common Limits Exam Errors; the worked mathematics is evidence for the idea, not a substitute for it.
Use this page to name the idea in words, connect it to the notation, and explain why the method works before treating it as a pattern.
Common Exam Errors and Their Repairs
| Error | Why it fails | Repair |
|---|---|---|
| Using the filled point as the limit | The point gives , not nearby behavior | Trace the graph from both sides first |
| Calling the answer | It is an indeterminate form | Simplify, then substitute again |
| Cancelling terms across addition | Cancellation applies to factors | Factor the entire numerator or denominator |
| Ignoring left and right sides | Two-sided limits require agreement | Compute both one-sided limits |
| Writing at negative infinity | The principal square root is nonnegative | Use for |
| Using degrees in | The fundamental limit is a radian statement | Convert or use radian measure |
| Applying IVT without continuity | Jumps can skip intermediate values | State continuity on the entire closed interval |
| Claiming IVT gives the exact root | It gives existence only | Use bisection or another numerical method for location |
| Using l'Hospital's Rule too early | It may be unavailable, circular, or hide the needed algebra | Use first-unit methods requested by the course |
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Original instruction with traceable references.
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