1. For each function below find a formula for the nth derivative of f(x) evaluated at -a. In other words, find f (a). Then use your formula to find the associated Taylor Series for each of the functi...

Question

Question

1. For each function below find a formula for the nth derivative of f(x) evaluated at -a. In other words, find f (a). Then us

Answer 1

Answer #1

niつ 2.1 2_ ml M-p ( χ-3 ナ n-tl a-3 M1 2i (-リ 2 -P 2 ot 2 h 사 2n)?

Answer 2

Similar Homework Help Questions

Solve the Taylor Series. 1. (a) Use the root test to find the interval of convergence of-1)* に0 (b) Demonstrate that the above is the taylor series of f()- by writing a formula for f via taylor'...

Solve the Taylor Series. 1. (a) Use the root test to find the interval of convergence of-1)* に0 (b) Demonstrate that the above is the taylor series of f()- by writing a formula for f via taylor's theorem at α-0. That is write f(x)-P(z) + R(x) where P(r) is the nth order taylor polynomial centered at a point a and the remainder term R(x) = ((r - a)n+1 for some c between z and a where here a 0. Show...
Assume that f(x) is a function whose nth derivative is given by (-1)"2" (2n)!(x + 1)+1...

Assume that f(x) is a function whose nth derivative is given by (-1)"2" (2n)!(x + 1)+1 2 using sigma notation and find the radius of Given the Taylor series of f(x) centered at a convergence.
Assume that f(x) is a function whose nth derivative is given by (-1)"2" (2n)!(x + 1)*+7...

Assume that f(x) is a function whose nth derivative is given by (-1)"2" (2n)!(x + 1)*+7 Given the Taylor series of f(x) centered at a = 2 using sigma notation and find the radius of convergence.

1. Answer the following questions. Justify your answers. a. (8pts) Find the Taylor series for f(x)...

1. Answer the following questions. Justify your answers. a. (8pts) Find the Taylor series for f(x) = (5x centered at a = 1 using the definition of the Taylor series. Also find the radius of convergence of the series. b. (8pts) Find a power series representation for the function f(x) = 1 5+X C. (4pts) Suppose that the function F is an antiderivative of a function f. How can you obtain the Maclaurin series of F from the Maclaurin series...
(5 pts) Consider the function f(x) = 8e7x. We want to find the Taylor series of...

(5 pts) Consider the function f(x) = 8e7x. We want to find the Taylor series of f(x) at x = -5. (a) The nth derivative of f(x) is f(n)(x) = At r = -5, we get f(n)(-5) = (c) The Taylor series at r = -5 is +00 T(x) = { (3+5)" n=0 = (d) To find the radius of convergence, we use the ratio test. an+1 L= lim n+too an and so its radius of convergence is R= |x...
15 Problem 12 (5 point) Assume that f(x) is a function whose nth derivative is given...

15 Problem 12 (5 point) Assume that f(x) is a function whose nth derivative is given by (-1)"2 (2n)!(x + 1)+1 Given the Taylor series of f(x) centered at a = 2 using sigma notation and find the radius of convergence

(5 pts) Consider the function f(x) = 8e7r. We want to find the Taylor series of...

(5 pts) Consider the function f(x) = 8e7r. We want to find the Taylor series of f(x) at x = x = -5. (a) The nth derivative of f(x)is f(n)(x) = 8(7)^ne^(7x) At = -5, we get f(n)(-5) = 8(7)^ne^-35 (c) The Taylor series at x = -5 is too T(x) = (3/7^n](^-35)n!/(n+ (x + 5)” n=0 (d) To find the radius of convergence, we use the ratio test. an+1 L= lim n+oo 1/(x+1) |x + 51 an and so...
Find the Taylor series of f(x) and determine the radius of convergence 1 f(z) center: 1+...

Find the Taylor series of f(x) and determine the radius of convergence 1 f(z) center: 1+ i 1+2z Expand the function f(z) in the Laurent series and determine the region of convergence f(z)= 1+z center: z -i Find all Taylor and Laurent series and determine the region of convergence. f() center: z1 Find the Taylor series of f(x) and determine the radius of convergence 1 f(z) center: 1+ i 1+2z Expand the function f(z) in the Laurent series and determine...
2 1. The Taylor series for a function f about x =0 is given by k=1...

2 1. The Taylor series for a function f about x =0 is given by k=1 Ikitt (a) Find f(")(). Show the work that leads to your answer. (b) Use the ratio test to find the radius of convergence of the Taylor series for f about x=0. c) Find the interval of convergence of the Taylor series of f. (a) Use the second-degree Taylor polynomial for f about x = 0 to approximate s(4)

2. The Taylor series of the function f(x) = - iſ about x = 0 is...

2. The Taylor series of the function f(x) = - iſ about x = 0 is given by (x − 2)(x2 – 1) 3 15 15 2. 63 4 F=3+ = x + x2 + x + x4 + ... (x − 2)(x2 - 1) 8 16 6 (a) (6 marks) Use the above Taylor series for f(x) = . T and Calcu- (x − 2)(x2 – 1) lus to find the Taylor series about x = 0 for g(x)...