MAT135H1 Lecture : Limits
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MAT135H1 Full Course Notes
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Q 2 n + q 3 n + . +p n n (cid:17) f(xi) x where f(x) = x lim n . 1 n i=1 i=1 n + (cid:16)q 1 q i np q i np np n 1 i1 (cid:0)13/2 03/2(cid:1) Find a function f and a number a such that f(t) t2 dt = 2. 6 + a x, for, all x > 0. Ther x a should look familiar from the statement of the fundamental theorem of calculus, and so you might think to di erentiate both sides. Then plug the result back into the original equation The solution is below, but try rst to do it with the hint. 0 + f(x)/x2 = 2 1 f (t) t2 dt. = d x) a f(x) = x 1/2x2 f(x) = x3/2. Now plug f(x) = x3/2 back into the left hand side of the given equation:
