Download presentation

Presentation is loading. Please wait.

Published byRosemary Lobb Modified over 2 years ago

1
Sec. 1.2: Finding Limits Graphically and Numerically

2
An Introduction to Limits Ex: What is the value of as x gets close to 2? Undefined ???

3
Sec. 1.2: Finding Limits Graphically and Numerically An Introduction to Limits Ex: x1.91.991.99922.0012.012.1 f (x) 2 12 2 11.4111.9411.994 undefined 12.006 12.06 12.61

4
Sec. 1.2: Finding Limits Graphically and Numerically An Introduction to Limits Ex:

5
Sec. 1.2: Finding Limits Graphically and Numerically An Introduction to Limits (informal) Definition: Limit If f (x) becomes arbitrarily close to a single number L as x approaches c from both the left and the right, the limit as x approaches c is L.

6
Sec. 1.2: Finding Limits Graphically and Numerically An Introduction to Limits Ex:

7
Sec. 1.2: Finding Limits Graphically and Numerically An Introduction to Limits Ex: 1

8
Sec. 1.2: Finding Limits Graphically and Numerically An Introduction to Limits Ex: In order for a limit to exist, it must approach a single number L from both sides. In order for this limit to exist, the limit from the right of 2 and the limit from the left of 2 has to equal the same real number (or height). DNE

9
An Introduction to Limits Ex: It would appear that the answer is – but this limit DNE because – is not a unique number. Sec. 1.2: Finding Limits Graphically and Numerically DNE

10
An Introduction to Limits Ex: Sec. 1.2: Finding Limits Graphically and Numerically DNE ZOOM IN

11
One-Sided Limits: Height of the curve approach x = c from the RIGHT Height of the curve approach x = c from the LEFT Definition (informal) Limit If the function f (x) becomes arbitrarily close to a single number L (a y-value) as x approaches c from either side, then the limit of f (x) as x approaches c is L written as * A limit is looking for the height of a curve at some x = c. * L must be a fixed, finite number.

12
Definition (informal) of Limit: If then (Again, L must be a fixed, finite number.)

13
Right and Left Limits To take the right limit, we’ll use the notation, The + symbol to the right of the number refers to taking the limit from values larger than 2. To take the left limit, we’ll use the notation, The – symbol to the right of the number refers to taking the limit from values smaller than 2.

14
Limits can be estimated three ways: Numerically… looking at a table of values Graphically…. using a graph Analytically… using algebra OR calculus (covered next section)

15
A limit does not exist when: 1. f(x) approaches a different number from the right side of c than it approaches from the left side. (case 1 example) 2. f(x) increases or decreases without bound as x approaches c. (The function goes to +/- infinity as x c : case 2 example) 3. f(x) oscillates between two fixed values as x approaches c. (case 3, example 5 in text: page 51)

Similar presentations

Presentation is loading. Please wait....

OK

Finding Limits Graphically and Numerically

Finding Limits Graphically and Numerically

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on seven segment display tutorials Ppt on instrument landing system mark Ppt on acute coronary syndrome definition Free download ppt on india of my dreams Ppt online mobile shopping Ppt on causes of 1857 revolt leaders Ppt on centroid and centre of gravity Ppt on world diabetes day circle Ppt on college management system Ppt on organizational culture and values.