# 1.02Introduction to limits - PowerPoint PPT Presentation

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1.02Introduction to limits. Speed limit  the speed which you can reach but not go over “I’ve hit my limit”  I’ve had enough, I can’t take any more In calculus, a limit is the intended value of a function. Definition of a limit. Example 1. Example 1. Example 1. Example 2.

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1.02Introduction to limits

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## 1.02Introduction to limits

Speed limit  the speed which you can reach but not go over

“I’ve hit my limit”  I’ve had enough, I can’t take any more

In calculus, a limit is the intended value of a function

### Example 2

A limit will not exist if the function is approaching an undefined value (ie ∞ )

### Example 3

means the limit approaching 3 from the right

means the limit approaching 3 from the left

### Right and left hand limits

For a limit to exist, the right-hand limit (RHL) and the left-hand limit (LHL) must both exist and must be equal

### Right and left hand limits

Therefore, the limit does not exist

• Limits can be evaluated 3 ways:

• Graphically

• Algebraically (several different method)

• Using the Sandwich Theorem (only some limits) also known as the squeeze theorem

### Evaluating limits

Use your graphing calculator to evaluate each of the following limits (calculator should be in RADIANS)

### Evaluating graphically with calculator

• From the Finney textbook

• P. 62 # 1 – 6

• P. 64 # 45 – 47 (instructions are on p. 63)