Expand the given function in a Maclaurin series. f(z) = e-5z 00 k = 0 5K (-1)K. K! R = ∞ X Give the radius of convergence R of the series.
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- Determine whether the sum of the infinite series is defined. 24+(12)+6+(3)+Find the MacLaurin Series for f (x) = cos(2/x) (-1)"(2x)" (2n)! -x+ 등-. 3 = 1 – x + 6 90 .. (-1)"(4x)" (2n)! = 1-2x + 을x2-.. 2 2 4 Zn=0 45 .. (-1)"x2" (2n)! .2 = 1 – * + - X. Zn=0 2 24 720 .. (-1)"x" (2n)! = 2 – x + - 100 3 Zn=0 720 ..The equivalent series for y(x) = E=3(n – 2)a,x" | is : A. En=o (n-1)an+3x"+3 B. En=0 (n - 1)an+2xn+2 C. En=0,(n- 5)an-3x"-3 D. En=0 (n+ 1)an+3x"+3
- What is the correct power series form of f(x) =V1-3x at a=0? (1.3.5.. (2n – 3)) · 3"x3n n= 0 2". n! Some other answer (1.3.5... (2n+1)) · 3^x³n 1- n= 2 2n. n! 3 (1.3.5. .. (2n– 3)· 3"x3n 1- n= 2 2". n! (1.3.5.. (2n+1)) · 3^x3n -Σ n= 0 2". n!The power series representation of f(x) = ln(x²-1) is given by A. ((-1)") - 1 X n+1 Pt B. None of the choices in this list. C. (-1) * "+1 −1Find the coefficients of the power series c0, c1, c2, c3, c4 for f(x)=ln(1-x^2)?The power series (-1)" 3 2n+1 n=0 at x=-1 is equal to 3 1 3/2Find a power series centered at -4 for f (x 7. 9-x n X-4 5 7 100 5 Zn=0 } (5) 7 100 п 9. n=0 9. 7 9 Zn=0 Σ-0 (4) 9. :)" 7 x+4 13Which of the following function has the Macularin series (-1)"4" x²n (-1)"4"n n=0 1 1 1 А. 4- x2 В. 4 + x2 С. 1- - 4.x2 1. D. 1+ 4x2 Е. 1+ 4x F. 1-4xRecommended textbooks for youAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage