MAT137Y1 Lecture : MAT 137Y 2007-08Winter Session, Self Generated Solutions to Problem Set 9.pdf
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MAT137Y1 Full Course Notes
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Mat 137y 2007-08 winter session, solutions to problem set 9. 1 (she 5. 2: the function f (x) = 1 x2 is decreasing on the interval [0,1], so mi = f (xi) and mi = f (xi 1) for all i. 64 : the function f (x) = cosx is decreasing on the interval [0, ], so mi = f (xi) and mi = f (xi 1) for all i. In similar fashion to the solutions above, we get. 12 : suppose p = {x0,x1, ,xn} is a regular partition of [a,b]. Then xk xk 1 = x for all k = L f (p) = (m1 + m2 + + mn) x, Uf (p) = (m1 + m2 + + mn) x. Therefore mi = f (xi) and mi = f (xi 1). Uf (p) l f (p) = x(cid:2)(cid:0) f (x0) + f (x1) + + f (xn 1)(cid:1) (cid:0) f (x1) + f (x2) + + f (xn)(cid:1)(cid:3)
