11.6.2. f(x, y) = x4 + y+ – a² – 2xy – y². - -

Q: if x~unif. (0,2),find the U.b. of p(lx - mul>= 2)

A: Given X~Unif(0,2) Result: if X~unif(a,b) then  Mean=(a+b)/2 Variance=(b-a)2/12

Q: 35 Find the extrem poinbs of Pcxy)=xy Subject to X+y=20.

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Q: 2. given that y = 0 at r=1

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Q: 19) * (xy)* = e ; f ind y' y' = [1+ In(xy)I y' = -y [1+ In Option 2 O Option 4 y' = [1- In(x None of…

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Q: (2) = [| (a) %3D h (b) Value(s) that are NOT in the domain of -

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Q: hether S={(x,y.=) eR' := =0}

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Q: 1 Integrate with respect to x. 4+ 25(3x +1)²

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Q: The tanh (2x) sech (2x) dx is equal to sech (2x) sech (2x) +C OA 3 10 OB. sech (2x) sech (2x) +C. 3…

A: Solution

Q: (8) Suppose f(x, y) = -x + y², x = s² +t°, y = 2s – 3t. Compute f, when s = 1 and t =-1. %3D

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Q: れお! /0 fi23)=4 4 (か) 2,十 F) Eanals it Ofiles)= 12 D Not if tha above

A: Given: Fx,y = x3y2 To find: Fx2,3 We know that Fxx,y is differentiation of Fx,y with respect to x ,…

Q: ー28- Sa Oclumina f dz sabishy cauchy- Reimon quakir f andlgove @ frz= J-2xy ti C-Xyz] +z* @ f(2)=…

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Q: -3 Evaluate the integral ſ² ſ² ſ²₁ xz(y + 1)dxdydz

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Q: 8. Evaluate the integral S xydx from x=3 to x=6 when x = 6cos0 and y = 2cose A. 9/7 B. 9/3 C. 5/3 D.…

A: Topic:- integration by substituting

Q: 3. If f(x, y, z)= In xyz te(3.0²), find f,,f, and f-· 4

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Q: 2/3 Determine the length of x=| for 0<ys2. Assume that y is positive.

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Q: 1 1 Select all the antiderivatives of f(x)=-+ %3D x² +1

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Q: 7. Find the most general antiderivative of the function 9 (z) = - z² +1

A: We use Trigonometry substitution to find anti derivative

Q: 11. Find two different antiderivatives of the function f(x) = 6x² +2ex. 1

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Q: 1. Evaluate the integral [(4z° +3z2 +2z– 6) dz

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Q: 1 Find the most general antiderivative of the function x3 + 4x

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Q: ==, j= 4 and x=0 about tue liney=5

A: Disk method: -  When the axis of revolution is the plane region's boundary and the cross-sectional…

Q: 13. - (In t ² )º t dt

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Q: 3 c3 4. Evaluate the integral S ex+ydydx '2

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Q: 2. A firm produces two goods in pure ompetition &amp; has the pllowing TR &amp; TC functions R= 15Q…

A: In this question, concept of optimization is applied. Optimization Mathematical optimization is the…

Q: 3. If z = f (x, y), where x = e“ – e® and y = e® – e", show that UTM UTM az az UTM X : az - ду dx…

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Q: If fufe.- fuave diffa Veubable at'xo eI fuave difle Veubable at Xo eI Pi:I R,ists-n prove O…

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Q: 9 Give with an not example of T: W≤X →Y, to XT Ext. .R. boundedag. - keše bes

A: Please find the solution innext step this is an non-example of Tietze extension theorem in Topology.

Q: In Exercises 5–12, find and sketch the domain for each function

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Q: Show for Re(z) > 1 ex – 1 dr = T(z)5(2). et – 1

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Q: 3+ Evaluate the integral: Se³+ cosh2x33+ cosh2xsinh2x dx (3e)³ 3+ sinh2x A + C 21n3 (3e)3 + sinh2x B…

A: Application of integration

Q: of fxyl = 3X-y+6 Subjected QI Find to x+y=4 extrume v alues

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Q: 8. Compute using the trig. substitution S x2 -dx (1–x²)1/2

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Q: S F(s) %3D (s+5)6

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Q: 1. What should be A for the path independent of (2,4) xy + ) 2Ay – x y? (1,2) Moreover evaluate the…

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Q: B/let Flx)=[X]-X,x E(-2,2).which valuesof x o E(X) continuaus?

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Q: 6. Find the fized point of flx) [-,1] where', on fa = (동) x-(올)x3

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Q: Find the antiderivative of: dt/(1-7t)^3 where  u = 1-7t

A: To find antiderivative

Q: 2 dt 22. Evaluate o v9– 2t² 2 dy 3-y³ 24. Evaluate o v8-y'

A: 22)I=∫0129-2t2dtt=32 udt=32 duI=∫29-9u2 32duI=2 ∫11-u2 duI=2 sin-1uI=2 sin-12 t301I=2 sin-1(23)

Q: 10- If f(u, v, w) is differentiable and u = x - y, v = y - z, and w = z - x, show that fe fe fe = 0.…

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Q: 3. If f(x,y,z)= In 4 xyz Ite t3y:²s²) , find f,,f, and f..

A: Given that: f(x,y,z)=lnxyz4+e-(3xy2z2)

Q: 19. f(x. y) In(1 - x - y) %3D

A: As per our company guidelines we are supposed to answer only the first question that you have…

Q: Find fCx) if flo)=0 and the tanGat (k,F CX) has ine af Slore x(x+2) a

A: Given for the function F(x), F(0)=0 and tangent line to F(x) at x,F(x) has slope xx2+23.

Q: 35 Find the extrem poinbs of Pcxry)=xy Subject to X+y=20.

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Q: 10 Evaluate the integral f 2x (x2 + 4) " dx using the substitution u = x² + 4. 2x (x² + 4)*" dx =|…

A: The given integral ∫2xx2+410dx

Q: 12 | g(t) dt = 30 4. 9(7) V3 9(12) = 4 12 g'(x) Evaluate: dr = 16 + (g(x))²

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Q: First and second derrivative of: In(x^3y^2)=x^2+y^3

A: Given: ln(x3y2)=x2+y3 Differentiate the function with respect to x.…

Q: d'y on of x

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