uiz 8 (Math 3A: Spring 2017) Name: _____________________________________ You will not receive full credit if you do not clearly show work as demonstrated in class. x 1. d Show that f ( t ) dt = f ( x ) is true for f (t) = 6t on the interval [ 0, x ] . dx a x a. First find F ( x ) = f (t) dt by using the limit definition of the definite 0 n integral, F(x) = lim f ( t k* ) t , on the interval [ 0, x ] . n k=1 (6 points) x b. d Now find f (t) dt by applying the limit definition of the derivative, dx 0 d F ( x + h) F ( x) F ( x ) = lim , to the result of part a. Show that the h0 dx h final result is f ( x ) . (4 points)