a) Compute the Maclaurin polynomial of degree two for f(x)=cos(x) b) Use the polynomial of part...
Question:
a) Compute the Maclaurin polynomial of degree two for {eq}f(x)=cos(x) {/eq}
b) Use the polynomial of part (a) to estimate {eq}cos(\frac{ \pi}{12}){/eq}
c) Compute the error made using the estimate from part (b) fro the value of {eq}cos(\frac{ \pi}{12}){/eq}
Maclaurin polynomial:
If f(x) can be differential 'n' times at 0 , the we define the nth maclaurin series for f(x) to be give by formula
{eq}f(x) = f(0) + xf'(0) + \frac{x^2}{2!}f''(0) + \frac{x^3}{3!} f'''(0) + \dots + \frac{x^n}{n!}f^n(0) {/eq}
This is the general formula for Maclaurin polynomial.
For determine the estimate value of given function substituting value of x in maclaurin polynomial.
Answer and Explanation: 1
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To find maclaurin polynomial and estimate error
a) To find Maclaurin polynomial
{eq}\displaystyle f(x) = \cos(x) \ \qquad \qquad \qquad f(0)= 1...
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Taylor & Maclaurin Series for Cos(x) | Solutions & Applications
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Chapter 30 / Lesson 3
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Learn how to find the cos(x) Taylor series and, subsequently, how to find the Maclaurin series for cos(x). Understand the applications of the Maclaurin series.
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