1. Section 2.6 Trigonometric Limits
MAT 1234 Calculus I
Section 2.6
Trigonometric Limits

2. HW
WebAssign HW 2.6

3. Preview
The Squeeze Theorem
Important Trigonometric Limits

4. The Squeeze Theorem x y a

5. The Squeeze Theorem y L x a

6. The Squeeze Theorem y L x a

7. The Squeeze Theorem You will see this type of idea over and
over again. L x a

8. Example 1
We cannot apply the limit laws since
DNE (Lab 2, 4(c))

9. Example 1
We cannot apply the limit laws since
DNE (Lab 2, 4(c))

10. Example 1
We cannot apply the limit laws since
DNE (Lab 2)

11. Example 1

12. Example 1

13. Expectations

14. Example 1

15. Important Limits
We are going to look ONLY the first limit today.

16. Important Limit
Use to find the formulas for the derivatives of the tri. functions
Use to find other limits
Use often in physics for approximations e.g. mechanical system, optics

17. Example Simple Pendulum
When the angle is small, the motion can be modeled by

18. Example 2
It can be shown that*
Apply the squeeze theorem.

19. Example 3

20. Example 4

21. Generalized Formula
Why?

22. Example 5

23. Remark It is incorrect to use the limit laws and write
since we do not know the existence of

24. Example 6

25. Do We Have Time?

26. Purposes (When Time Permits...)
Look at the interesting power of geometry.
Look at an application of the squeeze theorem.

27. Geometric Proof (Idea)

28. Simplified Proof:

29. Simplified Proof:

30. Simplified Proof:

31. Simplified Proof:

32. Important Limit

33. Important Limit