Homework SourseFind the Maclaurin series for fx x24e2xSolution Sorry heres
Find the Maclaurin series for f(x) = (x^2+4)e^2x
Solution
Sorry.. here\'s how u do it.. e^x = (1+ x + x^2/2! + x^3/3! +....) e^2x = 1+ 2x + (2x)^2/2!+ (2x)^3/3!+... = summation ( (2x)^(n-1) / n!) for n=1 to inf f(x)= (x^2+4) e^2x = (x^2+4) {summation ( (2x)^(n-1) / n!) for n=1 to inf} ={ summation (x^2 (2x)^(n-1) / n!) for n=1 to inf} +{summation ( 4(2x)^(n-1) / n!) for n=1 to inf} ={summation{ 2^ n-1 x^n+1/n!} +{summation ( 2^n+1 * x^(n-1) / n!) for n=1 to inf} =4 + (2^3 x/2!) + x^2 (2^1-1/1!) + x^3 (2^2-1/2! + 2^4+1 /4!) +...
