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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