Find the Maclaurin series of the function f(x) = (3x2) sin(7x) (f(x) = C3 = C4 =

Question

Explanation / Answer

f (x) = (3x^2)sin(7x) => f(0) = 0 => c0 = 0 f1 (x) = 3* [2*x*sin(7x) +7*x^2*cos(7x) ] =>f1 (0) = 3* [ 0 + 0 ] = 0 =>c2= 0 f3 (x) = 3*[ 2*sin (7x) + 28*x*Cos (7x) -49*x^2*sin (7x) ] =>f3 (0) = 3*[ 0 + 0 + 0 ] = 0 => c3 = 0 f4 (x) = 3*[ 42*cos (7x) + 294*x*Sin (7x) -343*x^2*Cos (7x) ] =>f4 (0) = 3*[ 42 + 0 - 0] = 126 => c4 = 126/(4*3*2) = 126/24 = 21/4 f5 (x) = 3*[ -488*sin (7x) - 2744*x*Cos (7x) +2401*x^2*sin (7x) ] =>f5 (0) = 3* [ 0 - 0 + 0 ] = 0 => c5 = 0 f6 (x) = 3*[ -6160*cos (7x) + 24010*x*Sin (7x) +16807*x^2*Cos (7x) ] =>f6 (0) = 3* [ -6160 + 0 + 0 ] = -18480 => c6 = -18480/6*5*4*3*2 = 77/3 Similarly c7 would be 0

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.