Find a geometric power series for the following functions, centered at 0, (a) by the technique shown in examples 1 and 2 (b) by long division:
1.) f(x) = [(1/2+x)]
2.) f(x) = [(4/3+x)]
3.) f(x) = [(2/5-x)]
Find a geometric power series for the following functions, centered at 0, (a) by the technique shown in examples 1 and 2 (b) by long division: 1.) f(x) = [(1/2+x)] 2.) f(x) = [(4/3+x)] 3.) f(x) = [(2/...
Find a geometric power series for the function, centered at 0, by the following methods Rx) - 2+x (a) by the technique shown in Examples 1 and 2 Rx) - (b) by long division (Give the first three terms.) Need Help? Read T alk te Tutor - 0/2 points Previous Answers LarCalcET6 9.9.004. Find a geometric power series for the function, centered at 0, by the following methods - 5- (a) by the technique shown in Examples 1 and 2...
15. Let f(x) = 2 . 2+x a) Find the power series representation of f(x) centered at o b) Use the power series representation to find ½ dx. 16. Find the Taylor Series for f(x) = sin (2x) centered at T.
15. Let f(x) = 2 . 2+x a) Find the power series representation of f(x) centered at o b) Use the power series representation to find ½ dx. 16. Find the Taylor Series for f(x) = sin (2x) centered...
Find the power series representation centered at c = -3 for f(x) 2 x+5
(d) f(x) = (1 + x) ln(1 + x) Hint: differentiate. (4) Expand the following functions into power series centered at 0 and find the radius of convergence. You can either use geometric series method, known expansions, or derivatives. You don't have to analyze the remainder.
4 Problem 2: Find the power series representation (centered at x = 0) and the interval of convergence for the function f(0) = 7 - 30
find power series for (1/(1+x^2)). use this power series to prove that the taylor series centered at x=0 for actan(x) is x -x^3/3 +x^5/5 -... (-1)^n ((x^2n+1)/(2n+1))...
(1 point) Find the first five non-zero terms of power series representation centered at x = 0 for the function below. f(x) = arctan(3) Answer: f(x) = + 0 1 /4 What is the radius of convergence? Answer: R= 4
(1 point) Find the first five non-zero terms of power series representation centered at x = 0 for the function below. f(x) = arctan(3) Answer: f(x) = + 0 1 /4 What is the radius of convergence? Answer: R= 4
2. Find a power series expression centered around a = 0 for each function, by manipulating simpler known power series. Please give your answer in sigma notation, (a) f(x) = 3 + x2 (b) f(x) = 5 - 30
. 11 1. Find a power series for the function f(x) = centered at c=0, and 2x2 - 7x-9 determine its interval of convergence. You may use 3x" =1+ x + x? + x +... = 1 . 1-X
(1 point) Find a power series centered at a = 0 for the function ln(1 + x) When you have found the series, enter the sum of the first five non-zero terms of the series. Find the radius of convergence R of the power series. R= 1 Use the power series you found above, to build a power series for the function f(x) = x? ln(1 + x). Again, enter the first five non-zero terms. What is the radius of...