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1.2 Finding limits graphically and numericallyPowerPoint Presentation

1.2 Finding limits graphically and numerically

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### 1.2 Finding limits graphically and numerically

Calculus has its limits

Objective:

- To solve limits numerically and graphically
- To analyze properties of limits

What is calc?

- Calc is the math of change– of velocities and accelerations
- Pre-Calc Calc
- Static Dynamic
- Constant velocity Velocity of accelerating objects
- Slope of a line Slope of a curve
- Area of a rectangle Area under a curve

What is calc?

- Calc is a limit machine
- Pre-calc Limits Calculus
- 2 main problems:
- Tangent line problem (Ch 2)
- Area problem (Ch 4)

Intuitive approach to limits

- A limit is an expected value
- The actual value may be different or undefined
- Actual value at x=1: Expected value at x =1:

More formally…

- If f(x) becomes arbitrarily close to a single number L as x approaches C from both sides, the limit of f(x) as x approaches c is L.
- Written as:

In other words

- Three things must happen for a limit to exist
- The limit from the right exists
- The limit from the left exists
- The limit from the right equals the limit from the left

Ways to look at calc

- Graphically
- Numerically
- Algebraically

Graphically

- To find limits, use a graph.

Numerically…

- Make a chart
at x= 2

Another example

- at x = 1

Graph by hand

- What is the limit at x=2

Why limits Do Not Exist (DNE)

- 3 main reasons
- 1. f(x) approaches different numbers from the right and left
- 2. f(x) increases or decreases without bound
- 3. f(x) oscillates between fixed values

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