1. Let f(x) = x³ and compute the Riemann sum of f over the interval [1, 2], using n = 5 subintervals and roundyour answers to two decimal places.(a) Choose the representative points to be the left endpoints of the subintervals.(b) Choose the representative points to be the midpoints of the subintervals.

The given function is .We need to find the Riemann sum of over the interval , using sub intervals…

Answered: Let f(x) = x³ and compute the Riemann…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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2. Use partial differentiation to approximate the following sum, not the individual radical. V81 + V26 Your answer
(LT2.a) Express the following sum in Sigma notation: 3 4 5 6 + + + +...+ 33 34 36 38 (LT2.b) Consider the following graph of a function g: T -2 2 -2- 4 क 2 17 324 (b) Evaluate the definite integral f g(x) dx. -4 To demonstrate mastery you must show your work. 6 (a) Write out the left Riemann sum L5 for g on the interval [-4, 6] and compute its value.
The following table is a record of speed at certain time of a toy car moving 3 on a straight line. Estimate the distance traveled by the car from t = 0 tot = 30 by finding the Right Riemann Sum and the Left Riemann Sum of the speed function and graph the rectangles in each scenario. The unit for the time is 1 minute and the unit for the speed is 1 meter/minute. 20 25 30 15 30 Time 10 Speed 18 24 26 22 10 20
Let f(x) = x², and compute the Riemann sum of f over the interval [3, 5], choosing the representative points to be the left endpoints of the subintervals and using the following number of subintervals (n). (Round your answers to two decimal places.) (a) Two subintervals of equal length (n = 2) (b) Five subintervals of equal length (n = 5) (c) Ten subintervals of equal length (n = 10) (d) Can you guess at the area of the region under the graph of f on the interval [3, 5]? 32.67 square units
Let f(x) = 3+sin(), x € [ 0,27] a) Show that f(x) has a unique fixed point p on [0, 2n]. b) How many iterations needed to approximate p so that the error < 10-3.
Let f(x) = x2, and compute the Riemann sum of f over the interval [3, 5], choosing the representative points to be the right endpoints of the subintervals and using the following number of subintervals (n). (Round your answers to two decimal places.) (a) two subintervals of equal length (n = 2) (b) five subintervals of equal length (n = 5) (c) ten subintervals of equal length (n = 10) (d) Can you guess at the area of the region under the graph of f on the interval [3, 5]? 32.67 square units
Let f(x) = x² and compute the Riemann sum of f over the interval [6,8], using the following number of subintervals (n). In each case, choose the representative points to be the midpoints of the subintervals. (Round your answers to two decimal places.) (a) Use two subintervals of equal length (n = 2). 226 (b) Use five subintervals of equal length (n = 5). 196.8 (c) Use ten subintervals of equal length (n = 10). 241.6 X (d) Can you guess at the area of the region under the graph of f on the interval [6, 8]? 128 X square units
a) Write the Riemann sum for the function f (x) = -x on the interval [-1,1]. b) Calculate the limit of the Riemann sum c) Check the result of (b) by definite integral.

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