MathematicsChapter 2: Limit, Continuity and Derivative
Limit Laws
Limits distribute over sums, products, quotients with nonzero denominator, and suitable powers.
Learning objectives
- State the rule for limit laws.
- Solve a limit laws problem step by step.
- Check the result, restrictions, notation, and units.
Statement
Limits distribute over sums, products, quotients with nonzero denominator, and suitable powers.
Where / symbols
- Limit laws
- Limits distribute over sums, products, quotients with nonzero denominator, and suitable powers.
CONCEPT AND RULE
Limits distribute over sums, products, quotients with nonzero denominator, and suitable powers.
METHOD
For limit laws, 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
lim(x->2)(3x2-x)=3(4)-2=10.
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 limit laws
- 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:
- lim(x->2)(3x2-x)=3(4)-2=10.
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
- Limit laws
- rule
- worked example
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Limit Laws
Sticky Notes · Formula and Worked Revision
Core Idea
- Limits distribute over sums, products, quotients with nonzero denominator, and suitable powers.
Rule / Formula
- Limits distribute over sums, products, quotients with nonzero denominator, and suitable powers.
Method
- Identify givens and restrictions.
- Write the rule.
- Substitute and simplify.
- Check the result.
Worked Example
- lim(x->2)(3x2-x)=3(4)-2=10.
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
- Limits distribute over sums, products, quotients with nonzero denominator, and suitable powers.
- Worked pattern: lim(x->2)(3x2-x)=3(4)-2=10.
- Final check: domain, sign, notation, units, and reasonableness.
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