Consider the function δ(x) = c() ( 1 − < x < , 0 otherwise. (4) find compute lim→0 z 1 −1 dxδ0 (x)f(x) (5) for an arbitrary smooth function f(x) by expanding f(x) in a series expansion in x. do the integral two ways: by evaluating the derivative of δ(x), and using integration by parts. take the limit → 0 after doing the integral.