" If "f(x)={[xe^(-alpha x),x<=0],[x+ax^(2)-x^(3),x>0];" where "a>0," then "

If f(x)={:{(xe^(-(1/(|x|) + 1/x)), x ne 0),(0 , x =0 ):} then f(x) is

If f(x)={:{(xe^(-(1/(|x|) + 1/x)), x ne 0),(0 , x =0 ):} then f(x) is

The graph of the antiderivative of f(x)=xe^((x)/(2)) passes through (0, 3), then the value of g(2)-f(0) is

If f R to R is defined by f (x) = {{:(( 2 sin x - sin 2x)/(2x cos x ) " if " x ne 0) , ( alpha " for " x =0 ):} then the value of alpha so that f is continuous at 0 is

If f'(x)=xe^(x) and f(0)=1, find f(x)