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1
Aim: What is the trig limit?
Do Now: Find the limit lim 𝑥→0 sin𝑥 1. lim 𝑥→0 cos 𝑥 2. 1 lim 𝑥→0 tan 𝑥 3.
2
All three function from do now are continuous at x = 0, therefore, the limit is a finite number
lim 𝑥→ 𝜋 tan 𝑥 =− lim 𝑥→ 𝜋 2 − tan 𝑥 = Left side limit ≠ right side limit lim 𝑥→ 𝜋 2 tan 𝑥 Does not exist
3
lim 𝑥→0 sin 𝑥 𝑥 = 1 lim 𝑥→0 1−cos 𝑥 𝑥 = 0
Memorize these two limits as formulas to apply other problems
4
lim 𝑥→0 1−cos 𝑥 sin 𝑥 lim 𝑥→0 1 sin 𝑥 ∙ 1−cos 𝑥 1 = lim 𝑥→0 𝑥 sin 𝑥 1−cos 𝑥 𝑥 = =1∙0=0 =2 lim 𝑥→0 sin 𝑥 2 cos 𝑥 𝑥 2 lim 𝑥→0 2tan 𝑥 2 𝑥 2 =2 lim 𝑥→0 sin 𝑥 2 𝑥 2 cos 𝑥 2 =2 lim 𝑥→ cos 𝑥 sin 𝑥 2 𝑥 2 =2 1∙1 =2
5
lim 𝑥→ sin 𝑥 𝑥 2 lim 𝑥→0 𝑥 cos 𝑥 lim 𝑥→0 tan 𝑥 2𝑥 𝟏 𝟐 lim 𝑥→0 𝑥 2 +3𝑥 sin 𝑥 3 lim 𝑥→0 cs𝑐 3𝑥 cot 𝑥 𝟏 𝟑
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