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# 1.2 Finding limits graphically and numerically - PowerPoint PPT Presentation

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

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## PowerPoint Slideshow about ' 1.2 Finding limits graphically and numerically' - hedwig-buckley

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### 1.2 Finding limits graphically and numerically

Calculus has its limits

• To solve limits numerically and graphically

• To analyze properties of limits

• 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

• Calc is a limit machine

• Pre-calc  Limits  Calculus

• 2 main problems:

• Tangent line problem (Ch 2)

• Area problem (Ch 4)

• A limit is an expected value

• The actual value may be different or undefined

• Actual value at x=1: Expected value at x =1:

• 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:

• 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

• Graphically

• Numerically

• Algebraically

• To find limits, use a graph.

• Make a chart

at x= 2

• at x = 1

• What is the limit at x=2

• 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