Math 1271, Summer 2010, Worksheet 26.11. Divide the interval 2 ≤ x ≤ 5 into 6 small subintervals. Let x∗k, k = 1, 2, 3, 4, 5, 6 denotethe midpoints of these subintervals. Find x∗1, x∗2, ··· , x∗6. Let f (x) = 2x2+ 3. Find f(x∗k) fork = 1, 2, 3, 4, 5, 6. What is the value of6Xk=1fa +2k − 12n(b − a)?2. Given thatPnk=1(2k −1)2=n3(4n2−1), suppose that f (x) = 2x2+ 3, a = 0, and b = 6.Find an expression fornXk=1fa +2k − 12n(b − a).3. Find the linear approximation for f(x) = x3/2at the point x = 100. Use this linearizationto find an approximate value for (98.4)3/2.4. Find the linearization L(x) of the function f(x) =√3x + 1 at the point x = 5. EvaluateL(x) at x = 5.04 and so obtain an estimate of the value of√16.12.1Math 1271, Summer 2010, Worksheet 26.2Find each of the following antiderivatives.1.Rx3x2+11dx2.R(ecos x)(sin x)dx3.R(cos3x)(sin x)dx4.Re(x2)(x)dx5.Rx cos(x2)dx6.R√2 + sin x(cos
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