Use substitution to find the Madaurin Series of f(x) = cosa 4x 802 2(2n)! 827 2n)...
Find a Maclaurin series for f(x). (Use (2n)! —for 1:3:5... (2n – 3).) 2"n!(2n-1) X Rx) = (* V1 +48 dt . -*** * 3 n = 2 Need Help? Read It Talk to a Tutor
Find the interval of convergence of the power series: 5) 00 2n -(4x – 8)" n n=1 E (n + 1)(x - 2)" (2n + 1)! n=0 7) 00 w n(x + 10)" (2n)! n=0
It is known that Fourier series of f(x)=Ixlis 2 cos(2n-1)x (2n-1)2 on interval [ - TT, TT). Use this to find the value of the infinite sum 1 + 1 25 49 1 1 + + +
If f(x) = 2x(sin x + cosa), find f'(x) = f'(1) -
1. Find the first four power series terms of f(x) e sinx and compare values of f(.2) with the value from the 2n+1 ex: Σ(-1)" and sinx2(-)" n! series. {3 decimal places) Multiple the series 1. Find the first four power series terms of f(x) e sinx and compare values of f(.2) with the value from the 2n+1 ex: Σ(-1)" and sinx2(-)" n! series. {3 decimal places) Multiple the series
5) Use zero through second order Taylor series expansions to predict f(2) for f(x) 21x3x2 4x+3 Use a base point at x 1
n=0 4. Using the power series cos(x) = { (-1)",2 (-0<x<0), to find a power (2n)! series for the function f(x) = sin(x) sin(3x) and its interval of convergence. 23 Find the power series representation for the function f(2) and its interval (3x - 2) of convergence. 5. +
Fourier Series MA 441 1 An Opening Example: Consider the function f defined as follows: f(z +2n)-f(z) Below is the graph of the function f(x): 1. Find the Taylor series for f(z) ontered atェ 2. For what values of z is that series a good approximation? 3. Find the Taylor series for this function centered at . 4. For what values ofェis that series a good approximation? 5, Can you find a Taylor series for this function atェ-0? Fourier Series...
4x (x4 12 for x 1 Use the power series for (1 + x*)-1 and differentiation to find the power expansion for f(x) = n 1
12 muk) Use the binomial series for [2 marks] Use the binomial series formula to find the coefficient of x" for n > 1, in the Maclaurin series of (1 + x)1/2 w (-1)"1.3.5.... (2n-3) 21-1 n! (-1)" 3.5.7..... (2n-1) 2"n! (-1)""2.4.6... (2n-2) 21-1 n! (-1)" 2.4.6.... (2n - 2) (-1)"-13.5.7.... (2n-1) 21-1 n! (-1)^-11:3:5.... (2n-3) ( (F) 2"n! 21n! (-1)-11.3.5. .... (2n-1) 29 n! (-1)3.5.7..... (2n-3) 2n!