Dr. Ching I Chen

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LHôpitals Rule, Improper Integrals, and Partial
Fractions

• Dr. Ching I Chen

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8.1 LHôpitals Rule (1) Indeterminate Form 0/0
(Theorem 1)
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8.1 LHôpitals Rule (2) Indeterminate Form 0/0
(Theorem 1)
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8.1 LHôpitals Rule (3) Indeterminate Form 0/0
(Example 1)
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8.1 LHôpitals Rule (4) Indeterminate Form 0/0
(Example 2)
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8.1 LHôpitals Rule (5) Indeterminate Form 0/0
(Theorem 2)
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8.1 LHôpitals Rule (6) Indeterminate Form 0/0
(Example 3)
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8.1 LHôpitals Rule (7) Indeterminate Form 0/0
(Exploration 1-1)
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8.1 LHôpitals Rule (8) Indeterminate Form 0/0
(Exploration 1-2)
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8.1 LHôpitals Rule (9) Indeterminate Form 0/0
(Exploration 1-3)
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8.1 LHôpitals Rule (10) Indeterminate Form 0/0
(Exploration 1-3)
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8.1 LHôpitals Rule (11) Indeterminate Form 0/0
(Example 4)
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8.1 LHôpitals Rule (12)Indeterminate Forms
?/?,?0,?- ? (Example 5a)
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8.1 LHôpitals Rule (13)Indeterminate Forms
?/?,?0,?- ?(Example 5b)
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8.1 LHôpitals Rule (14)Indeterminate Forms
?/?,?0,?- ?(Example 6a)
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8.1 LHôpitals Rule (15)Indeterminate Forms
?/?,?0,?- ? (Example 6b)
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8.1 LHôpitals Rule (16)Indeterminate Forms
?/?,?0,?- ?(Example 7)
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8.1 LHôpitals Rule (17)Indeterminate Forms
1?,00,?0
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8.1 LHôpitals Rule (18)Indeterminate Forms
1?,00,?0 (Example 8)
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8.1 LHôpitals Rule (19)Indeterminate Forms
1?,00,?0 (Example 9)
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8.1 LHôpitals Rule (20)Indeterminate Forms
1?,00,?0 (Example 10)
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8.2 Relative Rates of Growth (1) Comparing Rates
of Growth
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8.2 Relative Rates of Growth (2) Comparing Rates
of Growth
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8.2 Relative Rates of Growth (3) Comparing Rates
of Growth
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8.2 Relative Rates of Growth (4) Comparing Rates
of Growth
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8.2 Relative Rates of Growth (5) Comparing Rates
of Growth (Example 1)
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8.2 Relative Rates of Growth (6) Comparing Rates
of Growth (Exploration 1-1,2)
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8.2 Relative Rates of Growth (7) Comparing Rates
of Growth (Exploration 1-3)
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8.2 Relative Rates of Growth (8) Comparing Rates
of Growth (Example 2-a)
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8.2 Relative Rates of Growth (9) Comparing Rates
of Growth (Example 2-b)
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8.2 Relative Rates of Growth (10) Comparing
Rates of Growth (Example 3)
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8.2 Relative Rates of Growth (11) Comparing
Rates of Growth
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8.2 Relative Rates of Growth (12) Comparing
Rates of Growth (Example 4)
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8.2 Relative Rates of Growth (13) Order and
Oh-Notation
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8.2 Relative Rates of Growth (14) Order and
Oh-Notation (Example 5)
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8.2 Relative Rates of Growth (15) Order and
Oh-Notation
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8.2 Relative Rates of Growth (16) Order and
Oh-Notation (Example 6)
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8.2 Relative Rates of Growth (17) Order and
Oh-Notation (Example 7)
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8.3 Improper Integrals (1) Infinite Limits of
Integration
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8.3 Improper Integrals (2) Infinite Limits of
Integration
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8.3 Improper Integrals (3) Infinite Limits of
Integration
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8.3 Improper Integrals (4) Infinite Limits of
Integration (Example 1)
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8.3 Improper Integrals (5) Infinite Limits of
Integration (Example 2)
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8.3 Improper Integrals (6) Infinite Limits of
Integration (Example 3)
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8.3 Improper Integrals (7) Integrands with
infinite Discontinuities
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8.3 Improper Integrals (8) Integrands with
infinite Discontinuities
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8.3 Improper Integrals (9, Exploration 1)
Integrands with infinite Discontinuities
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8.3 Improper Integrals (10) Integrands with
infinite Discontinuities (Example 4)
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8.3 Improper Integrals (11) Integrands with
infinite Discontinuities (Example 5)
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8.3 Improper Integrals (12) Tests for
Convergence and Divergence
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8.3 Improper Integrals (13) Tests for
Convergence and Divergence (Example 6)
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8.3 Improper Integrals (14) Tests for
Convergence and Divergence (Theorem 3)
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8.3 Improper Integrals (15) Tests for
Convergence and Divergence (Example 7)
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8.3 Improper Integrals (16) Tests for
Convergence and Divergence (Theorem 4)
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8.3 Improper Integrals (17) Tests for
Convergence and Divergence (Example 8)
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8.3 Improper Integrals (18) Tests for
Convergence and Divergence (Example 9)
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8.3 Improper Integrals (19) Applications
(Example 10)
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8.3 Improper Integrals (20) Applications
(Example 11)
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8.4 Partial Fractions and Integral Tables (1)
Partial Fractions (Example 1)
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8.4 Partial Fractions and Integral Tables (2)
General Description of the Method
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8.4 Partial Fractions and Integral Tables (2)
General Description of the Method
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8.4 Partial Fractions and Integral Tables (3)
General Description of the Method (Example 2)
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8.4 Partial Fractions and Integral Tables (4)
General Description of the Method (Example 3)
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8.4 Partial Fractions and Integral Tables (5)
General Description of the Method (Example 4)
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8.4 Partial Fractions and Integral Tables (5)
General Description of the Method (Example 5)
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8.4 Partial Fractions and Integral Tables (6)
Integral Tables (Example 6)
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8.4 Partial Fractions and Integral Tables (7)
Trigonometric Substitutions
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8.4 Partial Fractions and Integral Tables (8)
Trigonometric Substitutions
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8.4 Partial Fractions and Integral Tables (9)
Trigonometric Substitutions (Example 7)
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8.4 Partial Fractions and Integral Tables (10)
Trigonometric Substitutions (Example 8)