12.1 Finding Limits Numerically and Graphically

1 / 15

# 12.1 Finding Limits Numerically and Graphically - PowerPoint PPT Presentation

We are asking “What numeric value does this function approach as it gets very close to the given value of x?” Numeric approach: Complete the table of values to estimate the value of the limit. 12.1 Finding Limits Numerically and Graphically.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about ' 12.1 Finding Limits Numerically and Graphically' - karl

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

We are asking “What numeric value does this function approach as it gets very close to the given value of x?”

Numeric approach:

Complete the table of values to estimate the value of the limit.

### 12.1 Finding Limits Numerically and Graphically

We are asking “What numeric value does this function approach as it gets very close to the given value of x?”

Graphic approach:

Consider the graph and the different types of limits:

Find

• Find
• Find
• Find

### 12.2 Limit Laws

EX. Evaluate the limit, if it exists

### 12.2 Limit Laws

EX. Evaluate the limit, if it exists

First check – does subbing in the

value of x take the denominator to 0?

EX. Evaluate the limit, if it exists

First check – does subbing in the

value of x take the denominator to 0?

### 12.2 Limit Laws

EX. Evaluate the limit, if it exists

First check – does subbing in the

value of x take the denominator to 0?

EX. Evaluate the limit, if it exists

First check – does subbing in the

value of x take the denominator to 0?

### 12.2 Limit Laws

Vocabulary:

secant line

AROC

constant function

constant slope

### 2.3 Average Rate of Change (AROC)

Wolfram Demo secant lines

### 2.3 AROC – given a graph

2.3 AROC – given the function

EX. 1

f(z) = 1 – 3z2; find AROC between

z = -2 and z = 0

EX. 2

g(x) = ; find AROC between

x = 0 and x = h

### 2.3 Increasing/Decreasing functions

Wolfram Demo Secant -> Tangent lines

### 12.3 IROC – Instantaneous Rate of Change

Note that in these problems we will use the letter ‘h’ to represent the distance away from the point where we are considering the tangent line (x)

12.3 IROC – algebraic examples

EX. 3

f(x) = 1 + 2x – 3x2; find the equation of the tangent line at (1, 0) two different ways.

Method 1: consider the limit as x approaches 1

b. Method 2: consider the limit as h approaches 0

Now use the point slope formula to find the line’s equation: slope = -4, goes through (1, 0)

12.3 IROC – algebraic examples

Let’s see if this makes sense graphically:

f(x) = 1 + 2x – 3x2; We calculated that

the equation of the tangent line at (1, 0) is y = -4x + 4

12.3 IROC – classwork practice

• f(x) = 1/x2; find the equation of the tangent line at (-1, 1) and graph the function and the tangent line requested. Use method 1 (look at the limit as x approaches -1)
• f(x) = ; find the equation of the tangent line at (4, 3) and graph the function and the tangent line requested. Use method 2 (look at the limit as h approaches 0)