Download presentation

Presentation is loading. Please wait.

Published byDestinee Ching Modified over 2 years ago

1
§2 Limits and continuity 2.1 Some important definitions and results about functions

2
Note: Note:

4
2.2 Limit of a function Given a function f(x), if x approaching 3 causes the function to take values approaching (or equaling) some particular number, such as 10, then we will call 10 the limit of the function and write In practice, the two simplest ways we can approach 3 are from the left or from the right.

5
For example, the numbers 2.9, 2.99, 2.999,... approach 3 from the left, which we denote by x→3 –, and the numbers 3.1, 3.01, 3.001,... approach 3 from the right, denoted by x→3 +. Such limits are called one-sided limits.

6
Example: We make two tables, as shown below, one with x approaching 3 from the left, and the other with x approaching 3 from the right.

7
2.3 One-Sided Limit We have introduced the idea of one-sided limits. We write

8
We write

9
2.4 Methods of finding One-Sided Limit 2.4.1 Left-hand Limit: c c-h h

10
2.4.2 Right-hand Limit: c h

11
2.5 The precise ( ) definition of Limit a L

12
Some important results

13
The Definition of Limit a L

15
Examples What do we do with the x?

16
Limit Theorems

17
The right-hand limit of f (x), as x approaches a, equals L written: if we can make the value f (x) arbitrarily close to L by taking x to be sufficiently close to the right of a. a L One-Sided Limits

18
The left-hand limit of f (x), as x approaches a, equals M written: if we can make the value f (x) arbitrarily close to L by taking x to be sufficiently close to the left of a. a M

19
Theorem

Similar presentations

OK

The Tangent and Velocity Problems The Tangent Problem Can a tangent to a curve be a line that touches the curve at one point? animation.

The Tangent and Velocity Problems The Tangent Problem Can a tangent to a curve be a line that touches the curve at one point? animation.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on lead poisoning Ppt on resistance temperature detector manufacturers Ppt on layers of soil Ppt on partnership act 1932 india Convert pdf ppt to ppt online viewer Ppt on single phase and three phase dual converter y Ppt on power line carrier communication Ppt on indian english literature Ppt on energy conservation in india Ppt on word association test psychology