Sketch the reglon R of integration and switch the order of Integration. 16 - y2 f(x, y) dy dx -2 4 -4 4 2 -4 -2 /16 - x2 f(x, Y) dy dx = f(x, Y) dx dy

Q: sec2 x dx sec2 x – 1 f.

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Q: Using substitution show y = 1+ Ce-t² is a solution to dy + 2ty = 2t dt

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Q: The result of the integration sign(t-t)8(2t - 1)dr is 1 A. B.sign(t -) C. 5(2t+1) D. sign(t +

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Q: Determine whether the functions given below are homogeneous or not. (a) f(x, y) =: x' +y' 2.ry +3y?…

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Q: Suppose the rule ²[ƒ(-2,−1)+4ƒ(−2,0) + ƒ(−2,1)+ ƒ (2,−1)+4ƒ (2,0)+ƒ(2,1)] applied to 12 solve f(x,y)…

A: Given: The rule, 23f-2,-1+4f-2,0+f-2,1+f2,-1+4f2,0+f2,1 is applied to solve ∫-11∫-22fx,ydxdy.   To…

Q: Q2: if it was Ø(x,y, z) = 3x²y – y°z³ Find the regression of this function at the point (1,-2,-1)

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Q: Integration using Algebraic Substitution x²dx 1) S Vx+2 3

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Q: Given the function, x = 3 + Vx? + y² , find y. Vx² +y² - X y Vx² + y? - > ア= y Vx? + y² + x ア= y Vx?…

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Q: adx - dy 0 y dx+ +Edy = 0

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Q: a. (xy + y²)dx+ (=

A: a. Given,       (xy+y2)dx+(x+2y-1)dy=0

Q: (c) The x-axis: x=y+1 2.

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Q: 3. Integration by parts: 3x d x (V3 2x+4

A: To find out the integration.

Q: of and dy For the function f(x,y) = In (8x + 9y), find - - of

A: partial derivative of two variable functions

Q: f(x, y, z) = tanxy xy;f,(1, 2, -2) %3D

A: Dear student, since you have posted multiple questions, as per our policy we will answer first…

Q: Maximize the function f(x, y, z) = x² – y², given that x² + 2y² + 3z² = 1. %3D

A: Here, we can use Lagrange multiplier to maximize f(x,y,z)=x2-y2 with constraint x2+2y2+3z2=1. Let…

Q: Find the local extrema of the following function. f(x,y) = - 8x-8xy-6y + 120x + 68y + 3 Find f,(x.y)…

A: Given f(x,y)= -8x²-8xy-6y²+120x+68y+3 So, fx(x,y)= -16x-8y+120=-8(2x+y-15) And fy(x,y)= -8x-12y+68=…

Q: t sect df 2/ V3

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Q: ed help

A: Given,                       ∫C(y-x2)dsWhere C is the line segment from (4, 2) to (0, 0) followed by…

Q: (1) / va 4x2 – 4x – 3dr (f)

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Q: x3 dx 0 vx*+1 1

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Q: dy d²y Find аnd dx the first and second derivatives, for #2 & 3: dx2 • 2. y = 2x2 + 3x + 1 3. y =…

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Q: fipr + rp ( 0. - (zcsc

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Q: FTnd the General/Practical solution FoT +he Following DTFFerentiat equation. {x-9x? + 16x - 144)y?dy…

A: The differential equation is given as x3-9x2+16x-144y2dy=2x2-1e4ydx find the general solution.

Q: [ to y²-Xy flo dy 2

A: 1st we will use substitution and then integration by parts   ∫u.v dx=u∫v dx -∫dudx∫v dxdx

Q: Using Range-Kutta 4th order method, evaluate the following equation dy 1+2y2 +y4, y(0) = 0 for x =…

A: The given problem is to find the values of function at x=0.2 and x=0.4 for the given initial value…

Q: (4x+3)dr æ(x+1)(x-3)

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Q: C:y 2x, x 8 ing (x² + y³)dx + (2xy +3)dy1

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Q: dw 3. (w² +4)Z

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Q: dy - ¿°cax-4) .y(5) - D dx

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