Calculus:

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Calculus

• Has its limits

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Limits what are they?Height that a function
intends to reach What is happening to a
function as it approaches a certain point?
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How to find the limit?

1. Numerically- a table of values
2. Graphically- visual representation of values

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Definition of the limit of a function

• Lim f(x) L
• x-gt a
• the limit of f(x), as x approaches a, equals L
• to summarize, this says that the values of f
  (x) get closer and closer to the number L as x
  gets closer and closer to the number a (from
  either side of a), but x does not equal a.

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Numeric Method
X gt 1 f(x)
Xlt 1 F(x)

• Lim X-1
• x2 - 1

0.5 0.666667
0.9 0.526316
0.99 0.502513
0.999 0.500250
0.9999 0.500025
1.5 0.400
1.1 0.476190
1.01 0.497512
1.001 0.499750
1.0001 0.499975
X -gt 1
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• Graphic Approach

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(1,0.5)
0
2
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A limit that Fails to Exist

• As t
  approaches 0 from the left, H(t)
  approaches 0. as t 0 from the right,
  H(t) approaches 1. there is no single
  number that H(t) approaches as t
  approaches 0. therefore the limit
  does not exist.

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• Calculusphobe.com
• Precalculus, Watson, Stewart, and Redlin