Using the Sandwich theorem to find

Using the Sandwich theorem to find

If we graph , it appears that

Unfortunately, neither of these new limits are defined, since the left and right hand limits do not match. Unfortunately, neither of these new limits are defined, since the left and right hand limits do not match. If we graph , it appears that We might try to prove this using the sandwich theorem as follows: We will have to be more creative. Just see if you can follow this proof. Don’t worry that you wouldn’t have thought of it.

P(x,y) 1 (1,0) Unit Circle

T P(x,y) 1 O A (1,0) Unit Circle

multiply by two divide by Take the reciprocals, which reverses the inequalities. Switch ends.

By the sandwich theorem: p

Using the Sandwich theorem to find

Using the Sandwich theorem to find

Presentation Transcript

The Sandwich Generation

Using the fundamental theorem of Algebra!!!

Using Pythagoras’ Theorem

Ham sandwich theorem by Changqing Li

The Sandwich Mrs. Lombardo’s approach to using sources in writing

The Paragraph Sandwich

The Sandwich Miss Williams’ approach to using sources in writing

Using SAS To find

SOLUTION USING THEVENIN’S THEOREM

Using Parallelism to Improve Theorem Prover Interactivity

The Sandwich Generation

Proving the Pythagorean Theorem Using Similarity

The Confidence Sandwich

Using Simulations to understand the Central Limit Theorem

Use the Pythagorean Theorem to find a Leg

Using tiles to prove pythagoras' theorem

Using the Fundamental Theorem of Algebra!!!

The Source Sandwich

The Ham-Sandwich and the Brouwer Fixed Point Theorem

Example 1: Using the Pythagorean Theorem