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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1.02Introduction 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


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)

homework


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