Tentukan suku Pertama hingga suku ketiga dari deret MacLaurin fungsi h(x) = (cos x) ln (1+x)

Posted by andi telaumbanua on Jul 28, 2018 in Matematika |
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Tentukan suku Pertama hingga suku ketiga dari deret MacLaurin fungsi
h(x) = (cos x) ln (1+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:
cos x = 1 – x^2/2!+x^4/4!-x^6/6!+⋯
ln(1+x)= x-x^2/2+x^3/3-x^4/4+⋯

Sehingga deret MacLaurin dari h(x) = (cos x) ln (1+x) adalah

h(x) = (cos x) ln (1+x)

h(x) = (1 – x^2/2!+x^4/4!-x^6/6!+⋯) (x-x^2/2+x^3/3-x^4/4+⋯)

h(x) = x – x^2/2!+x^3/3-x^4/4– x^3/2!+x^4/4-x^5/6+x^6/8+x^5/4!-x^6/48+⋯

h(x) = x – x^2/2-x^3/6-x^4/4+x^4/4-3x^5/24+(5x^6)/48+⋯

h(x) = x – x^2/2 – x^3/6 – 3x^5/24 + (5x^6)/48 +⋯

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