6.3 Taylor polynomials hug the function near the center · Power Series, Second Half · Visual Calculus

6.3Taylor hugs

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Chapter 2 · Applications of Integration

2.1-2.2Areas & Slicing

2.3-2.4Shells & Arc Length

2.5Physical Applications

2.6Centers of Mass

2.7-2.9Log, Exp & Hyperbolic

Chapter 3 · Techniques of Integration

3.1-3.4Techniques I

3.5-3.7Techniques II

Chapter 5 · Sequences and Series

5.1-5.3Sequences & Series I

5.4-5.6Sequences & Series II

Chapter 7 · Parametric Equations and Polar Coordinates

7.1-7.2Parametric Curves

7.3-7.4Polar Curves

Chapter 6 · Power Series

6.1-6.2Power Series I

6.3-6.4Power Series II

6.3Taylor hugs 6.3Coefficient ladder 6.3Remainder bound 6.4Binomial series 6.4Series table 6.4Series integral 6.4Pendulum series

Home Calculus IISections 6.3-6.46.3 Taylor polynomials hug the function near the center

6.3

Taylor polynomials hug the function near the center

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exp5

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SymPy check = 2.7182818285

SymPy checks

Maclaurin series for e at x=12.7182818285

Taylor value for 1/x at x=3/20.6666666667

Cuberoot Taylor remainder bound0.03125

Binomial series value for sqrt(1.5)1.2247448714

Maclaurin arctangent value at 10.7853981634

Gaussian area from 0 to 10.7468241328

Pendulum k^2 correction coefficient0.25