Use the divergence theorem to calculate the flux integral F F.ds, where S is the outward-oriented boundary of the box given by 0 ≤ x ≤ 9,0 ≤ y ≤ 5,0 ≤ z ≤ 9, and F = (4x²y, −z², x² z² + 6y²z²). Enter an exact answer. Provide your answer below: SfF.ds=[

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Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of I f(x) = [*²₂ √t²³ +4³dt…

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Q: lim √x ln x X x+0+

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Q: Find the roots of (D4 + D² + 1) +1+√³ 1 ± √√√3 1± √3 2 2 -1 ± √3 2 - 0 1 + −1+ - 1 ± i√√3 2 e. none…

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Q: 5. Find the area of the region. a. One petal of r=2cos 30 d. Interior of r=1-sin

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Q: (D3-4D2)y = 5, Find Yp O a. 5x² 4 O b. 5x² 4 O C. 5x² 12 O d. 5x² 12 O e. none

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Q: Question 9 (D2 + 5D + 4)y = 3 - 2x, Find Yp a. 11 8 O b. O C. 11 d. 11 11 8 8 ४ | 3 O e. none + 8/3…

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Q: and V. 35. 36. 37. = (1,1,1), V = (2,0,1) = (1, -2, 1), V=(3,2,1) =(5, 0, 2), v= (-3,0,7)

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A: NOTE: Refresh your page if you can't see any equations. . An apple farm yields an average of 44…

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Q: Find the c value that satisfies the Mean Value Theorem. f(x) = 3 + √√x on the interval [0,4]

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Q: 10. dy_x²-3y² 2xy dx

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Q: 7. If y = (x³ - cos x), then y' = (A) 5(x³ - cos .x)* (B) 5(3x² + sin x) (C) 5(3x² + sin x) (D)…

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Q: Evaluate the integral. r1 7x dx

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Q: (D4-1)y= sinx, Find Yp O a. O b. 1 1 10 -sin 2x 15 -sin2x O c. 1 ➡cos2x 10 O d. 1 15 O e. none…

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Q: (D2 + 5D + 4)y = 3 - 2x, Find Yp O a. 11 8 O b. O C. O d. 11 8 11 8 11 X 8 3 + X O e. none 3 + X 3 X…

A: Given , (D²+5D+4)y= 3-2x So, yp=1/(D²+5D+4) {3-2x}

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A: g(x) = ∫0x(3 + sint) dtg'(x) = ddx∫03(3 + sin t)dt= (3 + sinx) ddx(x) - (3 + sin 0) ddx(0)=…

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Q: Given a = log, 5 and b = log, 4, use logarithmic properties to represent each of the following…

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Q: B. Eliminate the arbitrary constants in the equation y = C₁e²x+c₂e³ +6e". Use (a) elimination method…

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Q: Determine the solution of the following differential equations: y"" + 6y" + 12y' + 8y = 0; when x=0,…

A: According to question,Given Differential equation,y''' + 6y'' + 12y' + 8y = 0,when x= 0, y = 0, y'=…

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Q: Use the Ratio or Root Test to determine the convergence or divergence of the series. 5n-1 40 +7 n=1

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