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| Linear Approximation (Formula) |
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| Mean Value Theorem (Formula) |
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| Integral for Mass of a One Dimensional Object |
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| Integral for Work using Hook's Law |
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[image]
A(y) = cross-sectional area,
D(y) = distance the slice is lifted |
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| Integral for Force/Pressure |
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[image]
(a-y) = depth
w(y) = width |
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Divergence
[image]
*only proves divergence* |
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IF f(x) is continuous, positive, and decreasing
on interval [k,[image])
and [image]
Converges or Diverges
Then they both converge/diverge
[image] |
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Root Test
[image]
[image] |
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Ratio Test
[image]
[image] |
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Comparison Test
Given
[image]
[image] |
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Limit Comparison Test
Given
[image] |
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WITH [image] AND [image]
IF
[image] [image] [image] |
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Alternating Series Test
[image]
[image]
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When do Geometric Sequences Converge and Diverge?
[image] |
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