Curriculum
Pure Mathematics — Second Secondary
Unit 1: Real Functions and Curve Sketching
0/8
Unit 2: Exponents and Logarithms
0/12
Unit 3: Limits
0/6
Unit 4: Trigonometry
0/4
Text lesson
Limits at Infinity
Limits at Infinity
Common mistakes
Common mistakes
Key points
Treating ∞ as a numberdo not substitute ∞ directly. Rewrite the function first.
Dividing by the lowest power instead of the highestthe terms approach zero only when we divide by the highest power in the denominator.
Wrong answer when degrees are equalthe limit is not zero in that case. It is the ratio of the two leading coefficients.
Ignoring the directionthe limit as x → ∞ can differ from the limit as x → −∞, so check which direction is asked.
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