integralf(x)dx z be[f(a) + f(b). Let h = b-a The trapezoid rule for estimate an a)Derive the error for composite trapezoid rule b) Determine the minimum number of the subintervals needed to approximate (x+edr to an accuracy of at least 0.5 x 10-7 using the composite trapezoid rule

integralf(x)dx z be[f(a) + f(b). Let h = b-a The trapezoid rule for estimate an a)Derive the error for composite trapezoid rule b) Determine the minimum number of the subintervals needed to approximate (x+edr to an accuracy of at least 0.5 x 10-7 using the composite trapezoid rule

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

ChapterA: Appendix

SectionA.2: Geometric Constructions

Problem 10P: A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in...

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Question

integralf(x)dx z be[f(a) + f(b). Let h = b-a
The trapezoid rule for estimate an
a)Derive the error for composite trapezoid rule
b) Determine the minimum number of the subintervals needed to approximate
(x+edr
to an accuracy of at least 0.5 x 10-7 using the composite trapezoid rule

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A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in inches. a. Using the fact that the volume of the can is 25 cubic inches, express h in terms of x. b. Express the total surface area S of the can in terms of x.
A soda can is made from 40 square inches of aluminum. Let x denote the radius of the top of the can, and let h denote the height, both in inches. a. Express the total surface area S of the can, using x and h. Note: The total surface area is the area of the top plus the area of the bottom plus the area of the cylinder. b. Using the fact that the total area is 40 square inches, express h in terms of x. c. Express the volume V of the can in terms of x.
a. Use the Trapezoidal Rule to approximate the integral. (Round to four decimal places.) b. Estimate the error in using the approximation. Express the answer rounded to three decimal places. c. Determine the number n of subintervals needed to guarantee that an approximation is correct to within 0.0001
(a) Use the Trapezoidal Rule, with n=5 to approximate the integral ∫109cos(4x)dx T5= (b) The actual value of ∫109cos(4x)dx= (c) The error involved in the approximation of part (a) is ET=∫109cos(4x)dx−T5= (d) The second derivative f″(x)=The value of KK = max |f″(x)| on the interval [0, 1] = . (e) Find a sharp upper bound for the error in the approximation of part (a) using the Error Bound Formula |ET| ≤K(b−a^31/2n^2 (f) Find the smallest number of partitions nn so that the approximation TnTn to the integral is guaranteed to be accurate to within 0.001. n=