7 Consider the rational function (x) = Find the Taylor series at 0 of g(x) and...
What 2n 7. Determine the radius and interval of convergence of the power series function has this power series as its Taylor series at 07 (10) 27-1 8. Consider the rational function (x) Find the Taylor series at 0 of (2) and determine its radius and interval of convergence. (10) 2-1
(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...
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)
(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...
1 and determine its radius and interval of 9. Find the Taylor series at 0 of f(x) convergence. (10) 3+x
In(z) 3, Consider the function f(x)= (a) Find the Taylor series for r(z) at -e. b) What is the interval of convergence for this Taylor series? (c) Write out the constant term of your Taylor series from part (a). (Your answer should be a series!). (d) What can you say about the series you found in part (c), by interpreting it as the limit of your series as x → 0. (Does it converge? If so, what is the limit?)...
Consider the function f(x)-e a. Differentiate the Taylor series about 0 of f(x). b. Identify the function represented by the differentiated series c. Give the interval of convergence of the power series for the derivative. a. Choose the correct answer belovw 213 Ос. D. 2 41 61 b. The function represented by the differentiated series is Iill c. The interval of convergence of the power series for the derivative is Simplify your answer. Type an inequality or a compound inequality...
5. Find the Taylor series of the function f(x) - about x 3. x-7 (x +4) 3enti) . Find the interval of convergence of the series
Find a Taylor series about a =l for the function f (x)= . State the radius and interval of convergence.
13.) a.) Find the Taylor series for the function f(x) = e* centered at the point a = 2. Determine its interval of convergence. b.) Find the Maclaurin series for f(x) = x2e-X. Is this series convergent for x = 2? Explain.