9. X f(x) 2 -2 6 1 9 8 10 -4 15 3 The function f is continuous on the closed interval [2, 15] and has values as shown in the table above. Using the subintervals [2, 6], [6, 9], [9, 10], and [10, 15], what is the approximation of f₂5 f(x)dx found by using a left-Riemann sum?
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- 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 sums(a) Estimate the area under the graph of the function f(x)=1/(x+6) from x=0 to x=3 using a Riemann sum with n=10 subintervals and right endpoints. Round your answer to four decimal places. (b) Estimate the area under the graph of the function f(x)=1/(x+6) from x=0 to x=3 using a Riemann sum with n=10 subintervals and left endpoints. Round your answer to four decimal places.In this problem we will calculate the area between f(x)=9x^2+2 and the x-axis over the interval [0,4] using the limit of right-endpoint Riemann sums shown in the image. Express the following quantities in terms of n, the number of rectangles in the Riemann sum, and k, the index for the rectangles in the Riemann sum. A. We start by subdividing [0,4] into n equal width sub intervals [x0, x1], [x1, x2]..., [x n-1, xn] each of width delta-x. Express the width of each subinterval delta-x in terms of the number of subintervals n. B. Find the right endpoints x1, x2, x3 of the first, second, and third subintervals [x0, x1], [x1, x2], [x2, x3] and express your answers in terms of n. C. Find a general expression for the right endpoint xk of the kth subinterval [x k-1, xk], where 1 is less than or equal to k, which is less than or equal to n. Express your answer in terms of k and n. D. Find f(xk) in terms of k and n. E. Find f(xk)delta-k in terms of k and n. F. Find the value of the…
- 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 5.2. Suppose that f(x) is a function continuous for every value of x whose first derivative is f'(x) = 2(1-x)/1+x^2 and f"(x)= 4x(x^2-3)/ (1+x^2)^2 Further, assume that it is known that f has a horizontal asymptote at y = 0. and a. Determine all critical points of f.Determine the exact area of the region bound by the graph of f(x) = −x^2 + 5 and the x-axis on [−1,1] using a right-endpoint Riemann sum.
- What is the minimum value of f(x) = x^2 - 8 ln x on the interval [1,5]What is the area beneath the curve y=x2 +1 and above the x-axis from x = 0 to x = 4 by using the Right Riemann Sum using n = 4 and n=8Consider function g(x) = 4 - x2 on interval [0; 2]. Compute approximations to area under curve, using lower and upper Riemann sums, with regular partition P = {0; 1; 2}. PLOT AREAS
- 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?I got confused halfway and I emailed my professor except he wasn't much help with this problem. The question is: Consider the function f(x)=(x^2)/4+6. In this problem you will calculate ∫ [4,0] (x^2/4+6)dx by using the definition --> ∫[b,a] f(x)dx =lim(n→∞) ∑ni=1 f(xi)Δx. The summation inside the brackets is Rn which is the Riemann sum where the sample points are chosen to be the right-hand endpoints of each sub-interval. Calculate Rn for f(x)=(x^2)/4+6 on the interval [0,4] and write your answer as a function of n without any summation signs. You will need the summation formulas from your textbook. A) Rn = B) limn--> inf Rn =For the function f(x) = cos2 x on [0,pi] a) find the critical points on the given interval b) determine the absolute extreme values of f(x) on the given interval when they exist