Consider the given function. f(x) = c +8 Evaluate the Riemann sum for 0 ≤ x ≤ 2, with n = 4, correct to six decimal places, taking the sample points to be midpoints. Part 1 of 3 We must calculate M4= Since we wish to estimate the area over the interval [0, 2] using 4 rectangles of equal widths, then each rectangle will have width Ax= -1/2 X Part 2 of 3 We wish to find M4= x₂ = Since X₁, X₂, x3, x4 represent the midpoints of the four sub-intervals of [0, 2], then we must have the following. X1 0.25 1/4 x3 X4 = · Ĺ ‹(ׂ)µ× = [r(×₁) + f(×₂) + √(×3) + f(xa)]µ×, where X₁, X₂, X3, X4 represent the midpoints of four equal sub-intervals of [0, 2]. /=1 = (±)[^(×₁) + f(×₂) + √(×3) + f(×4)] · M4 = 0.75 ✔ 1.25 1.75✔ 3/4 5/4 7/4 Part 3 of 3 Using f(x) = ex + 8, we have the following. · ( ² ) [( ₁ + ₁) + (² + •)· ( √ - · 8) + (∞— + 8) + ( ∞ — + s)] (rounded to six decimal places) 1/2.
Consider the given function. f(x) = c +8 Evaluate the Riemann sum for 0 ≤ x ≤ 2, with n = 4, correct to six decimal places, taking the sample points to be midpoints. Part 1 of 3 We must calculate M4= Since we wish to estimate the area over the interval [0, 2] using 4 rectangles of equal widths, then each rectangle will have width Ax= -1/2 X Part 2 of 3 We wish to find M4= x₂ = Since X₁, X₂, x3, x4 represent the midpoints of the four sub-intervals of [0, 2], then we must have the following. X1 0.25 1/4 x3 X4 = · Ĺ ‹(ׂ)µ× = [r(×₁) + f(×₂) + √(×3) + f(xa)]µ×, where X₁, X₂, X3, X4 represent the midpoints of four equal sub-intervals of [0, 2]. /=1 = (±)[^(×₁) + f(×₂) + √(×3) + f(×4)] · M4 = 0.75 ✔ 1.25 1.75✔ 3/4 5/4 7/4 Part 3 of 3 Using f(x) = ex + 8, we have the following. · ( ² ) [( ₁ + ₁) + (² + •)· ( √ - · 8) + (∞— + 8) + ( ∞ — + s)] (rounded to six decimal places) 1/2.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 67E
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