PLUS Session 1 (Delta-Epsilon Limit Definition, The Pinching Theorem)

PLUS Session 1 (Delta-Epsilon Limit Definition, The Pinching Theorem)

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PLUS Session (Delta-Epsilon Limit Definition, The Pinching Theorem) Directions: For the next 30 minutes, work together in groups (3-4) on the following problems/questions. Afterwards, each group will present their solutions and answer questions relating to the correct answers. Everyone must work together! GOOD LUCK! Delta-Epsilon Limit Definition For ε > 0, find a δ > 0 such that | f ( x ) – L | < ε whenever 0 < | x – c | < δ. 1. 2. 3. Find the largest δ that “works” for ε = 0.1. 4. Find the largest δ that “works” for ε = 0.01.
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PLUS Session (Delta-Epsilon Limit Definition, The Pinching Theorem) Directions: For the next 30 minutes, work together in groups (3-4) on the following problems/questions. Afterwards, each group will present their solutions and answer questions relating to the correct answers. Everyone must work together! GOOD LUCK! Give a delta-epsilon proof for the following statements. 5. 6. The Pinching Theorem Recap of the Pinching Theorem:
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Unformatted text preview: PLUS Session (Delta-Epsilon Limit Definition, The Pinching Theorem) Directions: For the next 30 minutes, work together in groups (3-4) on the following problems/questions. Afterwards, each group will present their solutions and answer questions relating to the correct answers. Everyone must work together! GOOD LUCK! • Usually used to find the limit of a function that is too difficult to find (you can’t manipulate your limit using trig identities, conjugate form, etc…). Normally, use only when asked to. • Goal: find g ( x ) and h ( x ) that bound above and below your given function [ f ( x )]. • If you are given a function whose limit is easily determined, yet you are told to prove it by using the pinching theorem, then take advantage of that!! Find two functions above and below your given function that have the same limit as the one you know. Use the Pinching Theorem to solve the limit. 7. 8....
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This note was uploaded on 12/09/2011 for the course MATH 1501 taught by Professor N/a during the Fall '08 term at Georgia Institute of Technology.

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PLUS Session 1 (Delta-Epsilon Limit Definition, The Pinching Theorem)

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