Today’s topics and news

Today's topics and news

Topics: Formal proof of limits

Qin Deng

MAT137 Lecture 2.3

October 2, 2018 1 / 8

Today's topics and news

Topics: Formal proof of limits Homework for Wednesday: Watch video: 2.10 - 2.13

Qin Deng

MAT137 Lecture 2.3

October 2, 2018 1 / 8

Today's topics and news

Topics: Formal proof of limits Homework for Wednesday: Watch video: 2.10 - 2.13 Reminder: PS2 is due October 11th.

Qin Deng

MAT137 Lecture 2.3

October 2, 2018 1 / 8

Warm-up

1. Find a value of > 0 s.t. |x - 2| < = |2x - 4| < 1.

2. Find all values of > 0 s.t. |x - 2| < = |2x - 4| < 1.

3. Find all values of > 0 s.t. |x - 2| < = |2x - 4| < 0.1.

3. Give > 0, find all values of > 0 s.t. |x - 2| < = |2x - 4| < .

Qin Deng

MAT137 Lecture 2.3

October 2, 2018 2 / 8

An - proof

Goal

Prove

from the definition.

lim 2x = 4

x 2

1. Write down the formal definition of claim. This is the statement you will need to prove.

2. Write down the structure of the proof without details.

3. Write down the complete proof.

Qin Deng

MAT137 Lecture 2.3

October 2, 2018 3 / 8

Finding

1. Find all values of > 0 s.t. |x - 2| < = |x + 2| < 10.

2. Given > 0, find all values of > 0 s.t. |x - 2| < = |x - 2| < . 10

Qin Deng

MAT137 Lecture 2.3

October 2, 2018 4 / 8

Finding

1. Find all values of > 0 s.t. |x - 2| < = |x + 2| < 10.

2. Given > 0, find all values of > 0 s.t. |x - 2| < = |x - 2| < . 10

3. Given > 0, find many values of > 0 s.t. |x - 2| < = |x2 - 4| <

using your work from (1) and (2).

Qin Deng

MAT137 Lecture 2.3

October 2, 2018 4 / 8

An - proof

Goal

Prove

from the definition.

lim x2 = 4

x 2

1. Write down the formal definition of claim.

2. Write down the structure of the proof without details.

3. Write down the complete proof.

Qin Deng

MAT137 Lecture 2.3

October 2, 2018 5 / 8

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