MathematicsChapter 2: Limit, Continuity and Derivative
Types of Discontinuity
A discontinuity may be removable, jump, or infinite; classify it from one-sided behaviour.
Learning objectives
- State the rule for types of discontinuity.
- Solve a types of discontinuity problem step by step.
- Check the result, restrictions, notation, and units.
Definition
A discontinuity may be removable, jump, or infinite; classify it from one-sided behaviour.
Where / symbols
- Types of discontinuity
- A discontinuity may be removable, jump, or infinite; classify it from one-sided behaviour.
CONCEPT AND RULE
A discontinuity may be removable, jump, or infinite; classify it from one-sided behaviour.
METHOD
For types of discontinuity, identify the given information and required result. Select the matching definition or formula, state its conditions, substitute carefully, simplify one line at a time, and check.
WORKED EXAMPLE
A cancelled common factor creates a removable hole.
COMMON MISTAKE
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
How to solve types of discontinuity
- Identify the mathematical objects, givens, restrictions, and required result.
- Choose and write the relevant definition, theorem, or formula.
- Substitute with brackets and carry out one justified step per line.
- Simplify, state the final answer clearly, and verify it in the original setting.
Worked example
- Worked example:
- A cancelled common factor creates a removable hole.
In simple words
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
Key points
- Types of discontinuity
- rule
- worked example
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Types of Discontinuity
Sticky Notes · Formula and Worked Revision
Core Idea
- A discontinuity may be removable, jump, or infinite; classify it from one-sided behaviour.
Rule / Formula
- A discontinuity may be removable, jump, or infinite; classify it from one-sided behaviour.
Method
- Identify givens and restrictions.
- Write the rule.
- Substitute and simplify.
- Check the result.
Worked Example
- A cancelled common factor creates a removable hole.
Common Error
- Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
FBISE Exam Tip
- Show the formula, substitutions, algebra, restrictions, and final answer; method marks need visible reasoning.
60-second revision
- A discontinuity may be removable, jump, or infinite; classify it from one-sided behaviour.
- Worked pattern: A cancelled common factor creates a removable hole.
- Final check: domain, sign, notation, units, and reasonableness.
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