Section 2.6 Trigonometric Limits MAT 1234 Calculus I Section 2.6 Trigonometric Limits http://myhome.spu.edu/lauw

HW WebAssign HW 2.6

Preview The Squeeze Theorem Important Trigonometric Limits

The Squeeze Theorem x y a

The Squeeze Theorem y L x a

The Squeeze Theorem y L x a

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

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

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

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

Example 1

Example 1

Expectations

Example 1

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

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

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

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

Example 3

Example 4

Generalized Formula Why?

Example 5

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

Example 6

Do We Have Time?

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

Geometric Proof (Idea)

Simplified Proof:

Simplified Proof:

Simplified Proof:

Simplified Proof:

Important Limit

Important Limit