Homework SourseFind the first four nonzero terms of the Maclaurin series fo
Find the first four non-zero terms of the Maclaurin series for the function.
Enter terms in sequential order.
a) Sin^2(3x)
b) ln((1+6x)^12)
Enter terms in sequential order.
a) Sin^2(3x)
b) ln((1+6x)^12)
Solution
a) sin^2(0) + 2sin(0)cos(0)x + 2[-sin^2(0)+cos^2(0)]x^2/2! + 2[-2sin(0)cos(0)-2sin(0)cos(0)]x^3/3!+4[sin^2(0)-cos^2(0)]x^4/4!+4[2sin(0)cos(0)+2sin(0)cos(0)]x^5/5!+8[-sin^2(0)+cos^2(0)]x^6/6!+8[-2sin(0)cos(0)x^7/7!-2sin(0)cos(0)]x^8/8!+16[sin^2(0)-cos^2(0)]x^9/9! =
0 + 0 + x2 + 0 - (1/6)x4 + 0 + (1/90)x6 + 0 - (16/40320)x8 , (4 non-zero terms)
b) 12ln1 + (12x)/(1) - (12x^2)/[(1^2)(2!)] + (12x^3)/[(1^3)(3!)] - (12x^3)/[(1^4)(4!)]
0 + 12x - 6x2 + 2x3 - (3/4)x4 , (4 non-zero terms)
