`f(x){|iota n e^x| ; x<=-1 and [2+x]+[2-x] ; -1=1` ,where [.] is GIF.

If f(x) is polynomaial function of degree n, prove that int e^x f(x) dx=e^x[f(x)-f'(x)+f''(x)-f'''(x)+......+(-1)^n f^n (x)] where f^n(x)=(d^nf)/(dx^n)

If f(x) is polynomaial function of degree n, prove that int e^x f(x) dx=e^x[f(x)-f '(x)+f''(x)-f'''(x)+......+(-1)^n f^n (x)] where f^n(x)=(d^nf)/(dx^n)

Evaluate int f(x) is polynomaial function of then the degree, prove that int e^x f(x) dx=e^x[f(x) f'(x)+f^x=f^x+......+(-1)^n f^n (x)] where f^n(x) dx+(d^nf)/(dx^n)

If f(x)=|x-2| a n d g(x)=f[f(x)],t h e n g^(prime)(x)= ______ for x>20

If f(x)=|x-2| a n d g(x)=f[f(x)],t h e n g^(prime)(x)= ______ for x>20

f: R to R is a function defined by f(x) =(e^(|x|) -e^(-x))/(e^(x) + e^(-x)) . Then f is:

If f(x)={(sin3x)/x ,\ \ \ w h e n\ x!=0 1,\ \ \ w h e n\ x=0 . Find whether f(x) is continuous at x=0 .

If f: R^+ to R , f(x) + 3x f(1/x)= 2(x+1),t h e n find f(x)