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.
All three function from do now are continuous at x = 0, therefore, the limit is a finite number lim 𝑥→ 𝜋 2 + tan 𝑥 =− lim 𝑥→ 𝜋 2 − tan 𝑥 = Left side limit ≠ right side limit lim 𝑥→ 𝜋 2 tan 𝑥 Does not exist
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
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 2 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→0 1 cos 𝑥 2 sin 𝑥 2 𝑥 2 =2 1∙1 =2
lim 𝑥→ 0 + 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