Basic Limit Properties

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Basic Limit Properties

• Lesson 1.1.8

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• We know that a functions limit as x?c isnt
  always f(c).
• However, there are times when the limit is f(c).
• Well learn that and other shortcuts for
  figuring out limits.
• That way, you dont always have to graph or make
  a table of values.

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Learning Objectives

• Given a function and a point c, determine if the
  plug-in method is appropriate to find the limit
  as x?c and then find the limit.
• Given a function and a point c, evaluate the
  limit as x?c using arithmetic properties of
  limits.

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Plug-In Limits

• In Lesson 1.1.5, we learned that if a function is
  continuous at xc, then the limit as x?c is f(c).
• The functions on the next slide are always
  plug-in limits.

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Constant Function Limits

• a and b are both constants
• This means that for any constant function f(x)
  b, as x approaches any constant a, the limit will
  always be b.

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Linear Function Limits
The limit of f(x) x as x approaches any
constant is the constant itself.
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Exponential Function Limits
Just plug in a for x
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Example 1
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Limit Properties

• Let

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The Scalar Multiple Rule
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The Addition/Subtraction Rule
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The Multiplication Rule
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The Division Rule

• where

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Example 2

• Find the following limit

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Edison Online says

• You are supposed to separate the functions into
  f(x) x2 g(x) x1.
• Plug in 1 for both. You will get 1 and 2,
  respectively.
• Then apply the division rule to get your answer
  of ½.

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However

• For questions like these, if you just show me
  plugging in for the whole thing, I will not take
  off points.
• It is important to me that you simply know the
  properties and that you apply them when they are
  necessary.

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Example 3
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Wrap Up

• When finding the limit as x?c, if the function is
  continuous at c, just plug c in for x.
• Know your limit properties and apply them as
  necessary.

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Homework

• Textbook 1a,c,e 2b,d 3a