🪚Building🪚 the Taylor polynomial 👟step-by-step👟 #apcalculus #apcalc #unit10 #shorts

We look at how to build the 3rd degree Taylor polynomial for a given function. It's critically important to set up a structured chart. We start by filling our chart with necessary values: the first column lists n values corresponding to the degree of the polynomial we aim to build. The second column is n!, and the third column starts with the function itself, followed by successive derivatives down to the row matching our polynomial's degree.

The fourth column evaluates the functions in the third column at x=a, leading to the crucial fifth column where we divide the fourth column's results by the corresponding n! values. This provides us with the coefficients needed for our polynomial. With the chart complete, we proceed to construct the Taylor polynomial. This methodical approach ensures accuracy and simplifies the polynomial to its most concise form.

#TaylorPolynomial #CalculusTutorial #MathEducation #CalculusConcepts

Unit 10 of AP Calculus is all about Infinite Sequences and Series:
10.1 Defining Convergent and Divergent Infinite Series
10.2 Working with Geometric Series
10.3 The nth Term Test for Divergence
10.4 Integral Test for Convergence
10.5 Harmonic Series and p-Series
10.6 Comparison Tests for Convergence
10.7 Alternating Series Test for Convergence
10.8 Ratio Test for Convergence
10.9 Determining Absolute or Conditional Convergence
10.10 Alternating Series Error Bound
10.11 Finding Taylor Polynomial Approximations of Functions
10.12 Lagrange Error Bound
10.13 Radius and Interval of Convergence of Power Series
10.14 Finding Taylor or Maclaurin Series for a Function
10.15 Representing Functions as Power Series

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Видео 🪚Building🪚 the Taylor polynomial 👟step-by-step👟 #apcalculus #apcalc #unit10 #shorts канала Krista King