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High Performance Computer Architecture by Prof. Ajit Pal (NPTEL):- Lecture 21: Hierarchical Memory Organization

High Performance Computer Architecture by Prof. Ajit Pal (NPTEL):- Lecture 21: Hierarchical Memory Organization

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Ex: Find a Unit Vector in the Direction of a Given Vector in 3D

Ex: Find a Unit Vector in the Direction of a Given Vector in 3D

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Ex: Direction and Speed of a Plane in the Wind Using Vectors

Ex: Direction and Speed of a Plane in the Wind Using Vectors

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Converting Parametric Equation to Rectangular Form

Converting Parametric Equation to Rectangular Form

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Graphing Parametric Equations in the TI84

Graphing Parametric Equations in the TI84

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Introduction to Parametric Equations

Introduction to Parametric Equations

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Estimate a Definite Integral using a Power Series (Rational Function)

Estimate a Definite Integral using a Power Series (Rational Function)

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  • Date added May 16, 2018
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Determine the Function for the Sum of a Power Series

Determine the Function for the Sum of a Power Series

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Find the Sum of an Infinite Series Using a Known Power Series (sin(x))

Find the Sum of an Infinite Series Using a Known Power Series (sin(x))

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Find the Sum of an Infinite Series Using a Known Power Series (e^x)

Find the Sum of an Infinite Series Using a Known Power Series (e^x)

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  • Date added May 16, 2018
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Ex: Determine a Simplified Power Series for a Function Involving e^(ax)

Ex: Determine a Simplified Power Series for a Function Involving e^(ax)

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Differentiating and Integrating Using Power Series

Differentiating and Integrating Using Power Series

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Ex: Find a Power Series to Represent a Rational Function Using Differentiation

Ex: Find a Power Series to Represent a Rational Function Using Differentiation

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Ex: Find a Power Series to Represent a arctan(x) Using Integration

Ex: Find a Power Series to Represent a arctan(x) Using Integration

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Ex: Find a Power Series to Represent a Power Series Using a Product

Ex: Find a Power Series to Represent a Power Series Using a Product

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Ex 3: Find a Power Series to Represent a Power Series

Ex 3: Find a Power Series to Represent a Power Series

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Ex 2: Find a Power Series to Represent a Rational Function

Ex 2: Find a Power Series to Represent a Rational Function

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Ex 1: Find a Power Series to Represent a Rational Function

Ex 1: Find a Power Series to Represent a Rational Function

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Ex: Use a Maclaurin Polynomial for sin(bx^n) to Approximate an Integral

Ex: Use a Maclaurin Polynomial for sin(bx^n) to Approximate an Integral

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Ex: Find a Maclaurin Polynomial and the Interval for a Given Error - ln(1+x)

Ex: Find a Maclaurin Polynomial and the Interval for a Given Error - ln(1+x)

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Ex: Find a Maclaurin Polynomial and the Interval for a Given Error - cos(x)

Ex: Find a Maclaurin Polynomial and the Interval for a Given Error - cos(x)

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Ex: Find a Maclaurin Polynomial and Error of an Approximation - ln(cos(x))

Ex: Find a Maclaurin Polynomial and Error of an Approximation - ln(cos(x))

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Ex: Determine a Taylor Polynomial for a Square Root Function

Ex: Determine a Taylor Polynomial for a Square Root Function

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Determine the Maclaurin Series and Polynomial for Function in the Form ax^2*sin(bx)

Determine the Maclaurin Series and Polynomial for Function in the Form ax^2*sin(bx)

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Determine the Maclaurin Series and Polynomial for Function in the Form ax^2*e^(bx)

Determine the Maclaurin Series and Polynomial for Function in the Form ax^2*e^(bx)

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Determine the Maclaurin Series and Polynomial for Function in the Form a*cos(bx^2)

Determine the Maclaurin Series and Polynomial for Function in the Form a*cos(bx^2)

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Ex: Find a Degree One and Degree Two Maclaurin Polynomial

Ex: Find a Degree One and Degree Two Maclaurin Polynomial

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  • Date added May 16, 2018
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Ex: Find the Taylor Series of e^x

Ex: Find the Taylor Series of e^x

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Ex: Find the Taylor Series of x^3

Ex: Find the Taylor Series of x^3

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Ex 1: Maclaurin Series and Polynomial of cos(2x) / Find Approximation Error

Ex 1: Maclaurin Series and Polynomial of cos(2x) / Find Approximation Error

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  • Date added May 16, 2018
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Using Power Series Tables – Part 2

Using Power Series Tables – Part 2

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  • Date added May 16, 2018
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Using Power Series Tables – Part 1

Using Power Series Tables – Part 1

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Taylor and Maclaurin Series

Taylor and Maclaurin Series

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Ex 6: Interval of Convergence for Power Series (Not Centered at 0)

Ex 6: Interval of Convergence for Power Series (Not Centered at 0)

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Ex 5: Interval of Convergence for Power Series (Not Centered at 0)

Ex 5: Interval of Convergence for Power Series (Not Centered at 0)

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Ex 4: Interval of Convergence for Power Series (Centered at 0)

Ex 4: Interval of Convergence for Power Series (Centered at 0)

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Ex 3: Interval of Convergence for Power Series (Centered at 0)

Ex 3: Interval of Convergence for Power Series (Centered at 0)

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Ex 2: Interval of Convergence for Power Series (Centered at 0)

Ex 2: Interval of Convergence for Power Series (Centered at 0)

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Ex 1: Interval of Convergence for Power Series (Centered at 0)

Ex 1: Interval of Convergence for Power Series (Centered at 0)

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  • Date added May 16, 2018
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Representing a Function as a Geometric Power Series: Part 2

Representing a Function as a Geometric Power Series: Part 2

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Representing a Function as a Geometric Power Series: Part 1

Representing a Function as a Geometric Power Series: Part 1

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  • Date added May 16, 2018
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Power Series: Part 2

Power Series: Part 2

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Power Series: Part 1

Power Series: Part 1

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Taylor’s Theorem with Remainder

Taylor’s Theorem with Remainder

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  • Date added May 15, 2018
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Taylor Polynomials

Taylor Polynomials

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Ex: Number of Terms Needed in Partial Sum to Estimate an Infinite Sum with a Given Error

Ex: Number of Terms Needed in Partial Sum to Estimate an Infinite Sum with a Given Error

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Ex: Find the Error When Using a Partial Sum to Estimate an Infinite Sum (Alternating Series)

Ex: Find the Error When Using a Partial Sum to Estimate an Infinite Sum (Alternating Series)

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Ex 2: Determine if an Series and an Alternating Series Converge or Diverge

Ex 2: Determine if an Series and an Alternating Series Converge or Diverge

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Ex 1: Determine if an Series and an Alternating Series Converge or Diverge

Ex 1: Determine if an Series and an Alternating Series Converge or Diverge

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Ex: Determine if an Infinite Alternating Series Converges or Diverges (Divergent)

Ex: Determine if an Infinite Alternating Series Converges or Diverges (Divergent)

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Ex: Determine if an Infinite Alternating Series Converges or Diverges (Convergent)

Ex: Determine if an Infinite Alternating Series Converges or Diverges (Convergent)

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Ex: Apply Alternating Series to Infinite Series - Divergent

Ex: Apply Alternating Series to Infinite Series - Divergent

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  • Date added May 15, 2018
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Infinite Series: The Alternating Series Test

Infinite Series: The Alternating Series Test

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Ex 4: Determine if a Series Is Conditionally Convergent, Absolutely Convergent, or Divergent

Ex 4: Determine if a Series Is Conditionally Convergent, Absolutely Convergent, or Divergent

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Ex 3: Determine if a Series Is Conditionally Convergent, Absolutely Convergent, or Divergent

Ex 3: Determine if a Series Is Conditionally Convergent, Absolutely Convergent, or Divergent

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Ex 2: Determine if a Series Is Conditionally Convergent, Absolutely Convergent, or Divergent

Ex 2: Determine if a Series Is Conditionally Convergent, Absolutely Convergent, or Divergent

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Ex 1: Determine if a Series Is Conditionally Convergent, Absolutely Convergent, or Divergent

Ex 1: Determine if a Series Is Conditionally Convergent, Absolutely Convergent, or Divergent

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Conditionally and Absolutely Convergent Series

Conditionally and Absolutely Convergent Series

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Ex: Find a Partial Sum of a Alternating Series (Method #2)

Ex: Find a Partial Sum of a Alternating Series (Method #2)

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Ex: Find a Partial Sum of a Alternating Series (Method #1)

Ex: Find a Partial Sum of a Alternating Series (Method #1)

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  • Date added May 15, 2018
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The Alternating Series Test

The Alternating Series Test

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Ex 4: Infinite Series - The Ratio Test (Convergent)

Ex 4: Infinite Series - The Ratio Test (Convergent)

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Ex 3: Infinite Series - The Ratio Test (Convergent)

Ex 3: Infinite Series - The Ratio Test (Convergent)

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Ex 2: Infinite Series - The Ratio Test (Divergent)

Ex 2: Infinite Series - The Ratio Test (Divergent)

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Ex 1: Infinite Series - The Ratio Test (Convergent)

Ex 1: Infinite Series - The Ratio Test (Convergent)

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Infinite Series: The Ratio Test II

Infinite Series: The Ratio Test II

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Infinite Series: The Ratio Test I

Infinite Series: The Ratio Test I

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Ex 5: Infinite Series - The Root Test (Divergent)

Ex 5: Infinite Series - The Root Test (Divergent)

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Ex 4: Infinite Series - The Root Test (Convergent)

Ex 4: Infinite Series - The Root Test (Convergent)

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Ex 3: Infinite Series - The Root Test (Divergent)

Ex 3: Infinite Series - The Root Test (Divergent)

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Ex 2: Infinite Series - The Root Test (Divergent)

Ex 2: Infinite Series - The Root Test (Divergent)

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Ex 1: Infinite Series - The Root Test (Convergent)

Ex 1: Infinite Series - The Root Test (Convergent)

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The Ratio Test

The Ratio Test

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Infinite Series: The Root Test II

Infinite Series: The Root Test II

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Infinite Series: The Root Test I

Infinite Series: The Root Test I

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The Root Test

The Root Test

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Infinite Series: The Limit Comparison and Ratio Tests - Part 2

Infinite Series: The Limit Comparison and Ratio Tests - Part 2

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Infinite Series: The Limit Comparison and Ratio Tests - Part 1

Infinite Series: The Limit Comparison and Ratio Tests - Part 1

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Infinite Series: The Limit Comparison and Direct Comparison Tests<

Infinite Series: The Limit Comparison and Direct Comparison Tests<

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Infinite Series: The Limit Comparison Test (Divergent)

Infinite Series: The Limit Comparison Test (Divergent)

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Ex: Infinite Series - Limit Comparison Test (Radical, Divergent)

Ex: Infinite Series - Limit Comparison Test (Radical, Divergent)

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Ex: Infinite Series - Limit Comparison Test (Divergent)

Ex: Infinite Series - Limit Comparison Test (Divergent)

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Ex: Infinite Series - Limit Comparison Test (Radical, Convergent)

Ex: Infinite Series - Limit Comparison Test (Radical, Convergent)

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Ex: Infinite Series - Limit Comparison Test (Geometric, Divergent)

Ex: Infinite Series - Limit Comparison Test (Geometric, Divergent)

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Ex: Infinite Series - Limit Comparison Test (Convergent)

Ex: Infinite Series - Limit Comparison Test (Convergent)

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The Limit Comparison Test

The Limit Comparison Test

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Ex: Infinite Series - Direct Comparison Test (Inconclusive)

Ex: Infinite Series - Direct Comparison Test (Inconclusive)

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Ex: Infinite Series - Direct Comparison Test (Divergent)

Ex: Infinite Series - Direct Comparison Test (Divergent)

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Ex: Infinite Series - Direct Comparison Test (Convergent)

Ex: Infinite Series - Direct Comparison Test (Convergent)

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Infinite Series: The Direct Comparison Test

Infinite Series: The Direct Comparison Test

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The Direct Comparison Test

The Direct Comparison Test

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Ex 2: Infinite Series - P Series Test (Divergent) and Find Partial Sum

Ex 2: Infinite Series - P Series Test (Divergent) and Find Partial Sum

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Ex 1: Infinite Series - P Series Test (Convergent) and Find a Partial Sum

Ex 1: Infinite Series - P Series Test (Convergent) and Find a Partial Sum

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Infinite Series: The p-Series Test

Infinite Series: The p-Series Test

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The p-series Test

The p-series Test

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Ex 6: Infinite Series - Integral Test Requiring Integration by Parts (Convergent)

Ex 6: Infinite Series - Integral Test Requiring Integration by Parts (Convergent)

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Ex 5: Infinite Series - Integral Test (Convergent Involving Arctangent)

Ex 5: Infinite Series - Integral Test (Convergent Involving Arctangent)

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Ex 4: Infinite Series - Integral Test (Exponential and Convergent)

Ex 4: Infinite Series - Integral Test (Exponential and Convergent)

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Ex 3: Infinite Series - Integral Test (Radical and Divergent)

Ex 3: Infinite Series - Integral Test (Radical and Divergent)

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Ex 2: Infinite Series - Integral Test (Rational Function and Divergent)

Ex 2: Infinite Series - Integral Test (Rational Function and Divergent)

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