Today’s topics and news

Today's topics and news

Topics: Intuitive and formal definition of a limit

Qin Deng

MAT137 Lecture 2.2

September 26, 2018 1 / 12

Today's topics and news

Topics: Intuitive and formal definition of a limit Homework for Tuesday: Watch video: 2.7 - 2.9

Qin Deng

MAT137 Lecture 2.2

September 26, 2018 1 / 12

Today's topics and news

Topics: Intuitive and formal definition of a limit Homework for Tuesday: Watch video: 2.7 - 2.9 Reminder: PS1 is due 11:59PM Thursday. Make sure you are familiar with the submission system.

Qin Deng

MAT137 Lecture 2.2

September 26, 2018 1 / 12

Today's topics and news

Topics: Intuitive and formal definition of a limit Homework for Tuesday: Watch video: 2.7 - 2.9 Reminder: PS1 is due 11:59PM Thursday. Make sure you are familiar with the submission system. Reminder: Deadline to switch to MAT135 is October 4th.

Qin Deng

MAT137 Lecture 2.2

September 26, 2018 1 / 12

Today's topics and news

Topics: Intuitive and formal definition of a limit Homework for Tuesday: Watch video: 2.7 - 2.9 Reminder: PS1 is due 11:59PM Thursday. Make sure you are familiar with the submission system. Reminder: Deadline to switch to MAT135 is October 4th. News: Proof clinic is open.

Qin Deng

MAT137 Lecture 2.2

September 26, 2018 1 / 12

Implications

Find all positive values of A, B, and C which makes the following implications true. 1. (x R,) |x - 3| < 1 = |2x - 6| < A. 2. (x R,) |x - 3| < B = |2x - 6| < 1. 3. (x R,) |x - 3| < 1 = |x - 3.5| < C .

Qin Deng

MAT137 Lecture 2.2

September 26, 2018 2 / 12

Proof exercise

For all A R. Ivan likes A if and only if a R s.t. x A, x a. Alfonso likes A if and only if a R s.t. x A, x < a.

Decide if the following statements are true or false. Prove your assertion. 1 For every A R, if Ivan likes A then Alfonso likes A. 2 For every A R, if Alfonso likes A then Ivan likes A.

Qin Deng

MAT137 Lecture 2.2

September 26, 2018 3 / 12

Limits from a graph

3

2

1

-4 -3 -2 -1 -1

y=f(x)

-2

-3

Find the value of

1234

1 lim f (x)

x 2

2 lim f (f (x))

x 0

Qin Deng

MAT137 Lecture 2.2

September 26, 2018 4 / 12

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