a) Explanation Calculation: Determine the value of ( 1 − x 2 ) − 1 2 . ( 1 − x 2 ) − 1 2 = ( 1 + ( − x 2 ) ) − 1 2 = { ( 1 ) − 1 2 + ( − 1 2 ) ( − x 2 ) + ( − 1 2 ) ( − 1 2 − 1 ) 2 ! ( − x 2 ) 2 + ( − 1 2 ) ( − 1 2 − 1 ) ( − 1 2 − 2 ) 3 ! ( − x 2 ) 3 + ⋅ ⋅ ⋅ } = 1 + x 2 2 + 3 x 4 8 + 5 x 6 16 Determine the series for the function sin − 1 x . d d x ( sin − 1 x ) = ( 1 − x 2 ) − 1 2 sin − 1 x = ∫ ( 1 − x 2 ) − 1 2 d x Substitute 1 + x 2 2 + 3 x 4 8 + 5 x 6 16 for ( 1 − x 2 ) − 1 2 b) To determine Find the first four non-zero terms of the Taylor series for the function cos − 1 x using part ( a ) result.

University Calculus: Early Transcendentals (4th Edition)

4th Edition

ISBN: 9780134995540

Author: Joel R. Hass, Christopher E. Heil, Przemyslaw Bogacki, Maurice D. Weir, George B. Thomas Jr.

Publisher: PEARSON

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Chapter 9.10, Problem 59E

To determine

Find the first four non-zero terms of the Taylor series for the function sin−1x using binomial series ddx(sin−1x)=(1−x2)−12 and also find the radius of convergence.

To determine

Find the first four non-zero terms of the Taylor series for the function cos−1x using part (a) result.

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Chapter 9.10, Problem 58E

Chapter 9.10, Problem 60E

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University Calculus: Early Transcendentals (4th Edition)

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Find the first four non-zero terms of the Taylor series for the function sin − 1 x using binomial series d d x ( sin − 1 x ) = ( 1 − x 2 ) − 1 2 and also find the radius of convergence.

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Find the first four non-zero terms of the Taylor series for the function sin−1x using binomial series ddx(sin−1x)=(1−x2)−12 and also find the radius of convergence.

Find the first four non-zero terms of the Taylor series for the function cos−1x using part (a) result.

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