Tentukan deret MacLaurin dari f(x) = e^x sin(x) 

Posted by andi telaumbanua on Jul 28, 2018 in Matematika |
Subscribe

Tentukan deret MacLaurin dari f(x) = e^x sin(x)

Jawab:

Deret MacLaurin;
f(x) = f(0) + f^1 (0)(x)+(f^2 (0))/2! x^2+(f^3 (0))/3! x^3+(f^4 (0))/4! x^4+⋯

Maka:

f(x) = e^x sinx
f^1 (x)= e^x sinx+e^x cos⁡x
f^2 (x)= e^x sinx+e^x cos⁡x+e^x cos⁡x-e^x sinx=2e^x cos⁡x
f^3 (x)= 2e^x cos⁡x-2e^x sin⁡x
f^4 (x)= 2e^x cos⁡x-2e^x sin⁡x -2e^x sin⁡x-2e^x cos⁡x= -4e^x sin⁡x

Maka:
f(0) = e^0 sin⁡0 = 0
f^1 (0)= e^0 sin⁡0+e^0 cos⁡0 = 0+1=1
f^2 (0)= 2e^0 cos⁡0= 2
f^3 (0)= 2e^0 cos⁡0-2e^0 sin⁡0=2-0=2
f^4 (0)= -4e^0 sin⁡0=0

Maka: deret macLaurinnya
f(x) = f(0) + f^1 (0)(x)+(f^2 (0))/2! x^2+(f^3 (0))/3! x^3+(f^4 (0))/4! x^4+⋯
f(x) = 0 + (1)(x)+2/2! x^2+2/3! x^3+0/4! x^4+⋯
f(x) = 0 + x+x^2+1/3 x^3+0+⋯
f(x) = x+x^2+1/3 x^3+⋯

Reply

Copyright © 2024 All rights reserved. Theme by Laptop Geek.