Calculus Chapter 2: Limits Section 2.6: Trig Limits and The Squeeze Theorem SWBAT: evaluate trig limits using the squeeze theorem. Standard: F.IF. Ø Understand the concept of a function and the use of function notation. “Do Now” Evaluate each limit: a) lim!→!
c) lim!→!
!!!!!!
!!!
! ! !!!!!
!!!
b) lim!→! ! cos 𝑥 tan 𝑥 d) lim!→!
! ! !!!!
!!!
Calculus Chapter 2: Limits Example: Show that lim 𝑥 sin
!→!
1
= 0 𝑥
We know that sin 𝑥 takes on values between −1 𝑎𝑛𝑑 1: Multiply the inequality by 𝑥 : Since, The Squeeze Theorem tells us that… Example: lim
!→!
𝑥 − 2 cos
1
𝑥−2
We know that cos 𝑥 takes on values between −1 𝑎𝑛𝑑 1: Multiply the inequality by (𝑥 − 2): Since, The Squeeze Theorem tells us that… Calculus Chapter 2: Limits Example: lim 𝑥 cos
!→!
1
𝑥
We know that cos 𝑥 takes on values between −1 𝑎𝑛𝑑 1: Multiply the inequality by 𝑥 : Since, The Squeeze Theorem tells us that… Closure: 1) What are the techniques that we’ve learned so far in order to estimate/calculate the limit of a function? 2) What should our first option always be when evaluating a limit? Homework: 1. Pg. 99 #’s 7 – 9, 11 2. Review Packet: All the Odds 3. Study for Quiz on 2.3, 2.5, and 2.6