1.- In the following problem, find the Riemann sum for the given function on the indicated interval. What is the norm ||P|| of the partition? S(x)=x , [0,4] , two subintervals; x, =0, x, 5 , x, =4 ; x =2 x;=3
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- If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local extremum offon (a,c) ?In this problem you will calculate the area between f(x)=2x^2 and the x-axis over the interval [0,5] using a limit of right-endpoint Riemann sumsCalculate the indicated Riemann sum S5, for the function f(x)=26−3x2. Partition [−4,6] into five subintervals of equal length, and for each subinterval xk−1,xk, let ck=xk−1+xk/2.
- I have real trouble solving how to find the sum-of-products expansion for the function F(x,y,z) given in the table below. x y z F(x,y,z) 1 1 1 0 1 1 0 1 1 0 1 0 1 0 0 0 0 1 1 1 0 1 0 1 0 0 1 0 0 0 0 01. Estimate the volume of the solid that lies below the surface z = xy and above the rectangle R = {(x,y) | 0 ≤ x ≤ 6, 0 ≤ y ≤ 4}.(a) using Riemann sum with m = 3, n = 2, and take the sample point to be the upper the right corner of each square(b) using midpoint rule with the same values of m and n in problem (a).1) Calculate the area (A) of the limit domain by the equation curve y=1/x, x=(n-1), x=(x+1) and the axis. n>1 2) By using the Simpson method, show that A= 1/3*((1/(n-1))+(4/n)+(1/(n+1))) We will divide the interval [(n-1),(n+1)] into 2 sub-intervals of equal length. 3) Show that ¦E¦ = 4/15n5 where E is the error made in order 5.
- Find the Riemann Sum for the function f(x)=12x+1 and the partition {0,2,5,8} using the sample points ξi={1,3,6}.Let f(x)=x2 defined on [0,1]. Let S5 be a Riemann sum for the function with 5 sub-divisions of equal length. By how much is the largest possible value of S5 greater than the smallest possible value of S5?calculate the indicated Riemann sum S5 , for the function f(x) = 29 -- 4x^2. Partition [ -1, 9 ] into five subintervals of equal length, and for each subinterval, let ck= (xk-1 + xk) / 2.
- Calculate the Riemann sum of the function F(x)= x2/11 in the interval (3,7) for a partition n=8 rectangles. Take into account the left end of each subintervalMy question is, if they intersect at -1 and 1, why are the limits integration set up for 0 to 1? And not -1 to 1?Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the given interval. y = x2/4 , [0, 6]