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CalculusMultivariable Calculus8th Edition

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Chapter 11, Problem 51RE
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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643

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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
Textbook Problem

Find the Maclaurin series for f and its radius of convergence. You may use either the direct method (definition of a Maclaurin series) or known series such as geometric series, binomial series, or the Maclaurin series for ex, sin x, tan−1 x, and ln(1 + x).

51. f(x) = sin(x4)

To determine

To find: The Maclaurin series for given function sin(x4) and its radius of convergence.

Explanation

Given:

The function is sin(x4) .

Result used:

The expansion of sinx is ∑n=0∞(−1)n1(2n+1)!x2n+1 . (1)

The radius of convergence of sinx is ∞ .

Calculation:

Consider the given function f(x)=sin(x4) .

Substitute x4 for x in equation (1),

sin(x4)=∑n=0∞(−1)n1(2n+1)!(x4)2n+1=

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For the 30-60-90 triangle shown, suppose that XZ=a. Find: a YZ b XY

Elementary Geometry For College Students, 7e

Convert the following mixed numbers to improper fractions. 15.

Contemporary Mathematics for Business & Consumers

Construct a difference table to predict the next term of each sequence. 1,4,21,56,115,204,...

Mathematical Excursions (MindTap Course List)

Approximating a Function Value In Exercises 39-44, approximate the function at the given value of x, using the ...

Calculus: Early Transcendental Functions (MindTap Course List)

Use the guidelines of this section to sketch the curve. y=tan1(x1x+1)

Single Variable Calculus: Early Transcendentals

Using Formulas In Exercises 77-82, find the indefinite integral by using the appropriate formula from Exercises...

Calculus of a Single Variable

Use the unit circle to evaluate each function. cos135

Trigonometry (MindTap Course List)

Find the decimal representation for each of the numbers in Exercises 1-6.

Elements Of Modern Algebra

If we know that then the absolute value of the nth remainder of the Taylor series for y = f(x) about a for is...

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

One of the vector forms of Green’s Theorem says that a) b) c) d)

Study Guide for Stewart's Multivariable Calculus, 8th

MODELING WITH DATA The following table gives the projected global defense spending in trillions of dollars from...

Finite Mathematics for the Managerial, Life, and Social Sciences

Prove the statements in Review Exercises 32 to 36 using analytic geometry. If the diagonals of a rectangle are ...

Elementary Geometry for College Students

Projectile Motion In Exercises 27-40, use the model for projectile motion, assuming there is no air resistance ...

Multivariable Calculus

Evaluating an Improper Integral In Exercises 3348, determine whether the improper integral diverges or converge...

Calculus (MindTap Course List)

Maximum Area A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular win...

Calculus

Round the following decimals to the indicated number of decimal places. 7.0.63165 (3 places)

Mathematics For Machine Technology

Describe, compare, and contrast the five research strategies (descriptive, correlational, experimental, quasi-e...

Research Methods for the Behavioral Sciences (MindTap Course List)

Solve each equation by completing the square. x28x+15=0

College Algebra (MindTap Course List)

Data from a survey of 1046 adults age 50 and older were summarized in the AARP Bulletin (November 2009). The fo...

Introduction To Statistics And Data Analysis

Describe what it means to say that science is empirical, public, and objective, and explain why each of these p...

Research Methods for the Behavioral Sciences (MindTap Course List)

In exercise 10, data showing the values of several pitching statistics for a random sample of 20 pitchers from ...

Statistics for Business & Economics, Revised (MindTap Course List)

Three firms carry inventories that differ in size. Firm As inventory contains 2000 items, firm Bs inventory con...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

In Exercises 2142, define the necessary symbols, rewrite the argument in symbolic form, and use a truth table t...

Mathematics: A Practical Odyssey

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