Calculate M4, the midpoint approximation, for f(x ) = x 2 + x for the interval [

Question

Calculate M4, the midpoint approximation, for f(x ) = x 2 + x for the interval [0,2]. If a1 = 3, a2 = - 1, a3 = 2, and a4 = 5, calculate the sums. ai (aj + (-1)ai) ak/ ak+1 (careful: the denominator is ak+1, not ak + 1!) Use the formulas given in the text for and to evaluate (4 + 3k - 2k2 +k3).(Be sure to use the given formulas. Don't write out the 10 terms and add them up. Think carefully about the 4!) Evalaute Find a formula for Rn, the right-endpoint approximation, for f(x ) = x2 + 1 on the interval [0,1]. Then compute the area under the graph by evaluating the limit of Rn as N rightarrow infinity. (Bonus question: worth 10 points. Total points for assignment not to exceed 100.) Using the formula given in the text for evaluate .

Explanation / Answer

2) a)3+(-1)+2+5=9 b) 9+3*(-1)+1=7 c) 3/(-1) + (-1)/2 + 2/5 = -3.1 3)answer = 4*10 + 3*[10*(10+1)/2] -2*[10*(10+1)*(2*10+1)/6] + [10*(10+1)]^2= 3890 4) 2/N^2 ?k = 2N(N+1)/N^2 =2(1/N+1).taking limit we get 2 since 1/N goes to 0 as N tends toinfinity Bonus question : answer = (1^2 + 2^2 +......+ 40^2) - (1^2 + 2^2 +......+ 20^2) =19270

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