Q. 1 TF Using $f(x) = \sin x$, constru... [FREE SOLUTION]

Chapter 8: Q. 1 TF (page 671)

Using $f(x) = \sin x$, construct the power series
${鈭�}_{K = 0}^{鈭�} \frac{f^{k} (0)}{k!} x^{k}$

Short Answer

Expert verified

The power series of the given function is :
$x - \frac{x^{3}}{3!} + \frac{x^{5}}{5!} - \frac{x^{7}}{7!} + . . . . . . . . .$

Step by step solution

Given Information

Given function is $f(x) =\sin x$.

Given power, series is to be constructed

$x-\frac{x^3}{3!}+\frac{x^5}{5!}-\frac{x^7}{7!}+...$

Here given form of power series is a Maclaurin series as the point at which the series is to be defined is zero.

$\oint_{a}^{b}x^{3}-x^{2}+\frac{4}{9}x$

Finding Maclaurin series of $f(x)=$sinx

Maclaurin series form is given by:

$\frac{f (0)}{0!} x^{0} + \frac{f^{1} (0)}{1!} x^{1} + \frac{f^{2} (0)}{2!} x^{2} + . . . . . . . .$

Here, f(x) = sin(x)

$f (0) = \sin (0) = 0$

$f^{1} (0) = \cos (0) = 1$

$f^{2} (0) = - \sin (0) = 0$

Substituting the above values in Maclaurin's general equation, we get:

$x - \frac{x^{3}}{3!} + \frac{x^{5}}{5!} - \frac{x^{7}}{7!} + . . . . . . .$

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91影视

Using \(f(x) = \sin x\), construct the power series
${鈭�}_{K = 0}^{鈭�} \frac{f^{k} (0)}{k!} x^{k}$

Short Answer

Step by step solution

Given Information

Finding Maclaurin series of \(f(x)=\)sinx

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91影视

Using \(f(x) = \sin x\), construct the power series鈭�K=0鈭�fk(0)k!xk

Short Answer

Step by step solution

Given Information

Finding Maclaurin series of \(f(x)=\)sinx

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Pure Maths

Geometry

Logic and Functions

Discrete Mathematics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Using \(f(x) = \sin x\), construct the power series
${鈭�}_{K = 0}^{鈭�} \frac{f^{k} (0)}{k!} x^{k}$