Curriculum
Course: Pure Mathematics — Second Secondary
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Curriculum

Pure Mathematics — Second Secondary

Unit 1: Real Functions and Curve Sketching

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Unit 2: Exponents and Logarithms

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Unit 3: Limits

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Unit 4: Trigonometry

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Text lesson

Finding Limits Algebraically

Pure Mathematics — Second Secondary

Finding Limits Algebraically

The indeterminate form 0/0

The indeterminate form 0/0

  • If direct substitution gives 0/0, no conclusion can be drawn yet, so the function must be simplified first.
  • There are two main methods:
Comparison aspectMain ideaKeywords
Factorisingfactorise the numerator and the denominator, then cancel the common factor that equals zero at the point. For example, x2 − 9 = (x − 3)(x + 3).factorisenumeratordenominatorthen
Multiplying by the conjugate
  • if a square root appears
  • multiply the numerator and the denominator by the conjugate
  • which is the same expression with the sign of the second term changed. For example
  • (√(x + 4) − 2)(√(x + 4) + 2) = x + 4 − 4 = x
squarerootappearsnumerator
Note
  • cancelling is allowed only for common factors of the whole numerator and denominator
  • never for separate added terms
cancellingallowedcommonfactors
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