Problem 1.31 Calculate the volume integral of the function T = z² over the tetra- hedron with corners at (0,0,0), (1,0,0), (0,1,0), and (0,0,1).

Q: Find the normal line for the level surface f(x,y,z) = 3x3 + cos (2y) + ln (2z) = c at the point…

A: f(x,y,z)=3x3+cos(2y)+ln(2z)-c=0Fx=9x2 , Fy=-sin(2y) , Fz=12z×2=1z∇F =<Fx,Fy,Fz >=<9x2,…

Q: 9. Explain how the Fundamental Theorem of Calculus Part 1 can tell us what the AP is as we compute…

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A: Divides the region into two subregions.

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A: Given function y=f(x) and f(x)≥0 for 0≤x≤4. and area bounded by y=f(x), y=0, x=0 and x=4

Q: 7) Suppose that y, =sinx and y, = cos x on [0,4] %3D Find the volume if the region between y, and y,…

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A: we will use shell method to find volume of solid of revolution

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Q: Evaluate each of the following partial integrals. 1. 2 co e*sinydxdy 2. (x + 2xy - 3y?)dydx II. 2e…

A: It is partial integral

Q: Let R be the region below bounded by the parabola y = 4 - x² and the lines 3x - 2y + 3 = 0 and y =…

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Q: Let R be the region that is below y=√x between x= 1 and x= 4. (a) Find the centroid of this region.…

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Q: Problem 9 Let f: R² → R be the function given by the function ƒ ( [*]) = x² + y + xy² + 4. Consider…

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Q: The volume of the solid obtained by rotating the region enclosed by I = 0, y= 1, 1= y? about the…

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Q: 1. Set up an integral for the volume of the solid enclosed by the following curves about the x-axis:…

A: We will answer the first question as we don't answer multiple questions at a time. Please resubmit…

Q: Given a solid whose cross-section is defined by A(x), the volume of the solid is given by А. V = [*…

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Q: (6) In this problem we will determine a formula for the volume of a pyramid with height h and a…

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