2. Limits and Derivatives Flashcards

1
Q

Definition
Limits of Functions

A
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2
Q

Lemma
Limits and Continuity

A
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3
Q

Theorem
Continuous and Sequential Limits

A
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4
Q

Theorem
Algebra of Limits

A
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5
Q

Definition
One-sided Limit

A
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6
Q

Definition
Infinite Limit

A
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7
Q

Definition
Limit at Infinity

A
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8
Q

Definition
The Derivative

A
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9
Q

Lemma
Differentiability and Continuity
Proof

A
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10
Q

Theorem
Sum and Product Rules
Proof

A
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11
Q

Lemma
Derivatives of Monomials
Proof

A
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12
Q

Theorem
Chain Rule
Proof

A
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13
Q

Lemma
Local Linearisation
Proof

A
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14
Q

Theorem
Mean Value Theorem
Proof

A
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15
Q

Corollary
Functions with Positive Derivative
Proof

A
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16
Q

Corollary
Functions with Zero Derivative

A

.

17
Q

Theorem
Rolle’s Theorem
Proof

A
18
Q

Theorem
Extrema and Derivatives

A
19
Q

Theorem
Derivatives of Inverses
Proof

A