Evaluate: S y? dV where E the solid hemisphere x² + y² + z²< 9 and y 2 0

Q: oS% (x? + y? + z*) dz dy dy

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A: Part A -  We can observe that the power in the expression on the right-hand side contains the…

Q: R 1. If OR 1 PQ at S, mLP = 30 and PO = 12 cm, Find PQ. %3D %3D

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A: Topic :- application of integration

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A: The given integral is                                         ∫Dx2+y2-9 dxdy Where…

Q: Name a secant. B. DF 2 回 [B] SY lal 32 [v] A

A: In geometry, a secant of a curve is a line that intersects the curve at a minimum of two…

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A: I use logarithmic differentiation with logarithmic properties

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Q: SS * dydx, y In x Where R is the rectangle 1 sx s e,-1sys2 Calculate

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Q: 2 x³ In(x?)dx

A: C. Trapezoidal rule with N = 10

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Q: ented square v V , (0, 1). The va + 8x² y dy)

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Q: Evaluate J by means of trapezoidal rule using n = 10 and n = 20: 1 J = exp(-x²)dx = Se

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Q: Evaluate II, (z*y +) dz dz dy, where D = [0, 1] × [0, 1] × [1, 2]. %3D

A: Here we have to find the integration if triple integrate: ∭x2y+1zdzdxdywhere D=0,1×0,1×1,2Thus it…

Q: -号。 - 4X u (x,o) =3 e 2 , ニ0 y2 Ansl ux,y) = 34(メ+) Ans.l ucx,y) 3 e %3D

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Q: ON 7 e the double integral || (8x+y)dA R rectangle R = {(x,y) : 0sxs5, 1s pe only the final answer.

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Q: dz where a inside r= C z-a 2ni

A: We have to find integration of given function Using Cauchy's Integral Formula.

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A: Multiple integrals

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Q: "ind where f(x, y, z) = e²´y and x = Vuv, y = ; %3D dv

A: To find the partial derivative using chain rule

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A: Residue theorem: The function f(z) is analytic inside a contour C except at z=a then the integral ∮C…

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Q: Q4: Find fr, fry fyx and fyy for f (x, y) = e*/y

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Q: a. The y' for y = (u – 4)z and u = x² + 4 b. The y' y = Vu and u = Vx

A: Given;          a.  y=u-432 and u=x2+4b.  y=u        and u=x a. Solve for y'…

Q: D Given: l, m antersect at P M <1 = 2x+5 m22 = X+5 %3D Pove: x= 50°

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Q: Find dy/dr if y = r In(x). Answer:

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Q: Evaluate [ ( (x2+ yz) dV, where R is the rectangular box 0 s x < 1,1 s y s 2,1 s z s2.

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Q: R 1. If OR 1 PQ at S, mLP = 30 and PO : 12 cm, Find PQ. %3D %3D

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Q: Find Jw Using te qppropriate chain rele sing w= x+y²+Z y=5t čos s where X =5t sins j 2=D9st

A: Given that, W=x2+y2+z2, Where x=5tsins, y=5tcoss, z=9st2 Calculate the value of ∂W∂s by using the…

Q: d' y Let y? 4x, then dx %3D

A: given  y2=4x differnciate with respect to x 2y dydx=4 dydx=42y=2yagain differntiate with respect to…

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Q: Evaluate ſ z dz, where C is given by x = 3t, y =t²; –1<t< 4.

A: Let us consider a complex function f(z) then the function can be written in the Cartesian coordinate…