Let k be a positive constant. Let u(x,t)=2kt1e(x)2/4tf()d, in which f is continuous on the real line. Show that u=kuzz for 0. Also determine u u(x,t) when f(x)=1 for all real x. Hint: Use a change of variables and the standard result that ew2dw=. Let k be a positive constant. Let u(x,t)=2kt1e(x)2/4tf()d, in which f is continuous on the real line. Show that u=kuzz for 0. Also determine u u(x,t) when f(x)=1 for all real x. Hint: Use a change of variables and the standard result that ew2dw=