Power Series – Finding The Radius \u0026 Interval of Convergence – Calculus 2
Power Series – Finding The Radius \u0026 Interval of Convergence – Calculus 2

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9-26. Taylor series and interval of convergence. Use the definition of a Taylor | Maclaurin series to find the first four nonzero terms of the Taylor series for the given function centered at a. Write the power series using summation notation. Determine the interval of convergence of the series:
10. f(x) = âˆša
11. f(x) = 2^a
12. f(x) = cos(2x), a = 0
13. f(x) = x
14. f(x) = x*sin(x), a = 0
15. f(x) = âˆš(x-1), a = 0
16. f(x) = ln(1 + 4x), a = 0
17. f(x) = 1/x
18. f(x) = (2x)^(-1), a = 0
19. f(x) = tan(1/2)
20. f(x) = sin(Ï€/4)
21. f(x) = 3^x, a = 0
22. f(x) = log(x + 1), a = 0

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04:45

Practice Exercises 9-26. Taylor series and interval of convergence Use the definition of a Taylor | Maclaurin series t0 find the first four nonzero terms Of the Taylor series for the given function centered at a. b. Write the power series using summation notation Determine the interval of convergence of the series:f)0 = |10. f(x)I1. fl) =ea =012 f(x) = COS 21, u13. fl)a = 0 mx)}14. f(x) =x sin Xa = 0

04:12

$13 – 20$ Find the Taylor series for $f ( x )$ centered at the given value of $a$ . I Assume that $f$ has a power series expansion. Do not show that $R _ { \mathrm { a } } ( x ) \rightarrow 0 . ]$ Also find the associated radius of convergence.

$$f ( x ) = \cos x , \quad a = \pi$$

04:55

$$f ( x ) = \sin x , \quad a = \pi / 2$$

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