1 02 introduction 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. 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 02 introduction to limits

1.02Introduction to limits


Definition of a limit

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 11

Example 1


Example 12

Example 1


Example 2

Example 2


Example 3

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

Example 3


Right and left hand limits

means the limit approaching 3 from the right

means the limit approaching 3 from the left

Right and left hand limits


Right and left hand limits1

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


Evaluating limits

  • 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


Evaluating graphically with calculator

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

Evaluating graphically with calculator


Homework

  • From the Finney textbook

    • P. 62 # 1 – 6

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

homework


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