Understanding Analysis Abbott

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Last updated 2:07 AM on 7/21/26
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14 Terms

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Definition of Differentiability

Definition 5.2.1

<p>Definition 5.2.1 </p>
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<p>If g: A → R is differentiable at a point..</p>

If g: A → R is differentiable at a point..

Theorem 5.2.3.

<p>Theorem 5.2.3.</p>
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<p>Algebraic Differentiability Theorem</p>

Algebraic Differentiability Theorem

Theorem 5.2.4

<p>Theorem 5.2.4</p>
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<p>Chain Rule</p>

Chain Rule

Theorem 5.2.5

<p>Theorem 5.2.5</p>
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<p>Interior Extremum Theorem</p>

Interior Extremum Theorem

Theorem 5.2.6

<p>Theorem 5.2.6</p>
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<p>Darboux’s Theorem</p>

Darboux’s Theorem

Theorem 5.2.7

<p>Theorem 5.2.7</p>
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<p>Rolle’s Theorem</p>

Rolle’s Theorem

Theorem 5.3.1

<p>Theorem 5.3.1</p>
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<p>Mean Value Theorem</p>

Mean Value Theorem

Theorem 5.3.2

<p>Theorem 5.3.2</p>
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<p>g’(x)=0 Corollary</p>

g’(x)=0 Corollary

Corollary 5.3.3

<p>Corollary 5.3.3</p>
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<p>f(x) = g(x) + k Corollary </p>

f(x) = g(x) + k Corollary

Corollary 5.3.4

<p>Corollary 5.3.4</p>
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<p>Generalized Mean Value Theorem</p>

Generalized Mean Value Theorem

Theorem 5.3.5

<p>Theorem 5.3.5</p>
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<p>L’Hospital’s Rule: 0/0 case</p>

L’Hospital’s Rule: 0/0 case

Theorem 5.3.6

<p>Theorem 5.3.6</p>
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<p>Definition Infinite Limit</p>

Definition Infinite Limit

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<p>L’Hospital’s Rule: ∞/∞ case</p>

L’Hospital’s Rule: ∞/∞ case

Theorem 5.3.8

<p>Theorem 5.3.8</p>