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Types of Discontinuity
A discontinuity may be removable, jump, or infinite; classify it from one-sided behaviour.
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Types of Discontinuity
What is it?
A discontinuity may be removable, jump, or infinite; classify it from one-sided behaviour.
In simple words
- 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.
Important terms
Types of discontinuity: A discontinuity may be removable, jump, or infinite; classify it from one-sided behaviour.
What you should learn
- State the rule for types of discontinuity.
- Solve a types of discontinuity problem step by step.
- Check the result, restrictions, notation, and units.
Recommended for Class 12
Full school-level explanation
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
How it works
- 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.
Remember
- Types of discontinuity
- rule
- worked example
- worked example
How the ideas connect
Worked example: A cancelled common factor creates a removable hole.
Deeper understanding
Go beyond memorising Types of Discontinuity. Connect the definition to reasons, relationships, exceptions, and exam wording.
How the ideas connect
Worked example: A cancelled common factor creates a removable hole.
Common mistakes
Exam focus
Core Idea
Rule / Formula
Method
Worked Example
Exam focus
Quick revision
- Types of discontinuity
- rule
- worked example
- 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
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
For long answers on Types of Discontinuity: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- Types of discontinuity
- rule
- worked example
- Types of discontinuity: A discontinuity may be removable, jump, or infinite; classify it from one-sided behaviour.
Important formulas
- Types of discontinuity
- rule
- worked example
Common exam traps
- Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
- A matching-looking formula is not valid until its conditions and domain have been checked.
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
- Mistake
A matching-looking formula is not valid until its conditions and domain have been checked.
- Mistake
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
Types of discontinuity
rule
worked example
Types of discontinuity: A discontinuity may be removable, jump, or infinite; classify it from one-sided behaviour.
A discontinuity may be removable, jump, or infinite; classify it from one-sided behaviour.
- Definition
- A discontinuity may be removable, jump, or infinite; classify it from one-sided behaviour.
- Critical warning
- Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all d
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Exam Practice
Define
Q1. Define Types of Discontinuity.
Explain
Q2. Explain: CONCEPT AND RULE.
Example
Q3. Give one clear example of Types of Discontinuity and say why it fits.
Mistake
Q4. State one common mistake students make about Types of Discontinuity.
Exam note
Q5. Write a short exam note on Types of Discontinuity: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.