Q: Use the second Taylor polynomial of f (x) = √
Use the second Taylor polynomial of f (x) = √x at x = 9 to estimate √9.3.
See AnswerQ: Show that ln [(1 + x)/(1 – x)]
Show that ln [(1 + x)/(1 – x)] = 2x + 2/3 x3 + 2/5 x5 + 2/7 x7 + … , | x | < 1. This series converges much more quickly than the series for ln(1 - x) in Example 3, particularly for x close to zero. Th...
See AnswerQ: The hyperbolic cosine of x, denoted by cosh x, is
The hyperbolic cosine of x, denoted by cosh x, is defined by cosh x = ½ (ex + e-x). This function occurs often in physics and probability theory. The graph of y = cosh x is called a catenary. (a) Use...
See AnswerQ: The hyperbolic sine of x is defined by sinh x =
The hyperbolic sine of x is defined by sinh x = ½ (ex - e-x). Repeat parts (a) and (b) of Exercise 23 for sinh x. Exercise 23: The hyperbolic cosine of x, denoted by cosh x, is defined by cosh x = ½...
See AnswerQ: Given the Taylor series expansion 1/√(1 + x)
Given the Taylor series expansion 1/√(1 + x) = 1 – ½ x + ½ * ¾ x2 - ½ * ¾ * 5/6 x3 + ½ * ¾ * 5/6 * 7/8 x4 - … , find the first four terms in the Taylor series of 1/√(1 - x) at x = 0.
See AnswerQ: Find the first four terms in the Taylor series of 1/√(
Find the first four terms in the Taylor series of 1/√(1 - x2) at x = 0.
See AnswerQ: Use Exercise 25 and the fact that ∫ 1/√(
Use Exercise 25 and the fact that ∫ 1/√(1 - x2) dx = ln(x + √(1 + x2)) + C to find the Taylor series of ln(x + √(1 + x2)) at x = 0. Exercise 25: Find the first four terms in the Taylor series of 1...
See AnswerQ: Use the Taylor series expansion for x/(1 - x)
Use the Taylor series expansion for x/(1 - x)2 to find the function whose Taylor series is 1 + 4x + 9x2 + 16x3 + 25x4 + … .
See AnswerQ: Use the Taylor series for ex to show that d/dx
Use the Taylor series for ex to show that d/dx ex = ex.
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