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Our heat-equation Green functionG(x,s)=e^(?x^2/4s)/(4?s)^1/2is very unusual whens approaches to 0

5. Our heat-equation Green function G(x, s) = e /48 / v47s is very unusual when s - 0. a. Show that the area under G(x, s) over all x is independent of the value of s. b. Show that if x2 > 0, lim, to G(x, s) = 0. c. Show that if f(x) has a McLaurin series, then lim 8-0 G(x, s) f(x) dx = f(0)