Question

xe3* Find the Maclaurin series for f (x) 5.

Answer 1

"Maclaurin xe^3x Taylor series: - Taylor series of function f(x) at a is defined as f(x) = a(a) + f'(a)/1! (x - a) + f""(a)/2! (x - a)^2 + f""'(a)/3! (x - a)^3 + Maclaurin series of function f(x) is a Taylor series of function f(x) at a = 0 f(x) = f(0) + f'(0)/1! (x) + f""(0)/2! (x)^2 + f""'(0)/3! (x)^3 + Ellipsis Find the derivatives of f(x) = xe^3x at a = 0 = 0 middot e^3 middot 0 + d/dx (xe^3x)(0)/1! x + d^2/dx^2 (xe^3x)(0)/2! x^2 + d^3/dx^3 (xe^3x)(0)/3! x^3 + 0 middot e^3 middot 0 = 0 d/dx(xe^3x) = d/dx(x) + e^3x + d/dx (e^3x)x = e^3x + e^3x middot 3x d/dx (xe^3x)(0) = e^0 + 0 = 1 \r\n d^2/dx^2 (xe^3x) d/dx(xe^3x) = e^3x + 3e^3x x d/dx (d/dx(xe^3x)) = d/dx (e^3x + 3e^3x x) = d/dx (e^3x) + d/dx (3e^3x x) = 3 middot e^3x + 3(e^3x + 3e^3x x)"