Q3) draw and find Df and Rf for y |x2 - 1|

Q: Evaluate p(x² + y²)5/2 dA, where D = {(x, y) E R² | 0 < y < 1, - V1- y² < a < 0}.

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Q: b. (1) (x) c. (fog)(x) d. (gof)(x)

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Q: rvdxdy ( R nd x 2 0, y 2

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Q: (b) where p = √x² + y². δ(x) δ(y) δ(ρ) Σπρ

A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: If r=lū'lgthere ñ'= nÎ+ y then find vy". Q.2. B nE R-

A: Given             r→ = xi^ + yj^ +zk^ then              r = x2 + y2 +z2 To find: ∇2 rn where r = r,…

Q: If y(z) = √3+ rºdr then 0 y' (2) = 524√√3+25 Q X estion E

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Q: f(r, y) : = V3x? + 4y? fz(3, – 2) =|

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Q: Q3) If f(x, y") = x + y? + Vãy find: af(x²y) and Ty) ду afxy)

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Q: (d) If F(x, y) = (4x² - y², -2xy), then f(x, y) =

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Q: Find ƒx (x, y)  and ƒy( x, y) .

A: Differentiate the function f(x,y)=ln|2x2+y2| with respect to x and keeping y as constant and carry…

Q: 3.2 find fxxy: flxiy) Bx*t 2€y?+ qxy!

A: when differentiate with x then y should be constant and when differentiate with y then x should be…

Q: Find & for f(r, y) = y- 4ry + 5y .3 2

A: Using partial derivative.

Q: If y = 3, then dy de 3x+2" |3|

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Q: dxdydz Evaluate 'V1-x? NI-x²-y² V1-x2-y?-z2

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Q: 9. Given that f(x, y) = xy² + x²y³ +x³y* (a) Find- (b) Find (c) Find

A: We are solving the first three subparts and for the next subparts questions post the question…

Q: Q- Find I. メー→! メー/ Vx -/

A: Evaluate

Q: Let f(x, y) = 160 2x2-3y² 2a? – For which value(s) of y is f(4, y) = 10? y =

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Q: Find &, for f(a, y) = xy? – 4.ry² +x*. 3

A: This question is related to partial derivatives.

Q: H.W: Find the domoin of y = X+3 4-[xt-q

A: Explanation of the solution is given below...

Q: f(x, y) = 3x – 2y x² + 2 + 2y? = 275

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Q: f(x, y) %3D (x? — 2у?)5 2y2)5

A: Consider the given function fx,y=x2-2y25   Partial derivative of f with respect to x…

Q: Express ow/ds in terms of r and s if w = x² + y², x=r-S, y=r+s A) 4s B) 4r C) 4sr O O

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Q: Q4: Find fur, fay, fyx and fy for f (x,y) = e*/y

A: Given: fx,y=exy To find: fxx, fxy, fyx and fyy

Q: 2b). Let y* + 5x2y² + yx = 624. A) Find y'

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Q: Find f'cx?, f"cxx) wheve fcK) = xe -2 Jc %3D

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Q: Given f(x, y) = - 5a4 – 4x²y³ + 6y°, find - fa(x, y) = fy(x, y) = %3D fez(x, y) =

A: As per our guidelines we are suppose to solve only first three sub-parts of a question. Kindly…

Q: If WX = 3t - 45 and VY = t, what is Y? W V Y こ

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Q: Q5: If f(x, y) = 6x, g(x,y) = x- 3y find Vf.Vg,V(fg)

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Q: Q5: If f (x, y) = 6x , g(x,y) = x - 3y find Vf,Vg,V(fg)

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Q: Q3) Given x(t) and (t) as below find and draw y(t) X(t) -1 -2 2 1 h(t) 2 2

A: ANSWER:

Q: if f(x,y) = √x² + y + 4, then find a a21 and ах ду х

A: If fx, y=x2+y+4, then to find ∂2f∂x2 and ∂2f∂y∂x.

Q: or the DE y' = xy2, y(0) = -1. Then, y(2)=

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Q: Q Evaluede ds where c is Linesegment fromcい3)のしら、-2)

A: Given integral is ∫c2x-y2ds from (1,3) to (5,-2)

Q: C1oy +11) dy ty2-4y+5 10)

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Q: (a) r'y"- ry + y = 2x, a>0

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Q: Evaluate | (r + y)ds, c : x 3t, y = - 3t + 3, for 0 <t< 3.

A: Given: ∫C(x+y)ds, C: x=3t, y=-3t+3, for 0≤t≤3

Q: f(x, y) = x³ – 2ry + 27y³.

A: Given: f(x,y)=x3-2xy+27y3 To find: Local extrema and saddle point of the function.

Q: |x² +y o'u is

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Q: f(x, y) = /322 + 5y²

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Q: Given f(x, y) = 4/32° + y + 8xy³, find f.(x, y) = f,(x, y) = |

A: Find the partial derivative of f(x,y) with respect to x to find fx(x,y) . Find the partial…

Q: if (y+ 4)² = x + 2, then + 2, then dy

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Q: Q3) If f (x, y²) = x² + y² + Vxy find : af(x².y) and f(x?y) ду ax

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Q: If it was p(x, y, z) = /x² + y2 + z? find V ?+

A: The formula for ∇2ϕ=∂2ϕ∂x2+∂2ϕ∂y2+∂2ϕ∂z2

Q: If x = t² and y = t³, then y O t 3/4t O 3/t Other: = ?

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Q: y ds, C: x = t², y = t, – 2 <t < 3

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Q: y Z. 4. If x = 13 and Y = 16°, find z. 5. If X = 19° and x = 11, find z.

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Q: Show that || Ar +b|3 cTx +d f(x) = {x |c"x +d > 0}, where A E RmXn, bE Rm, c€ R" and d e R.

A: As per the instruction, we will be solving part (b) of 3.23. We are given the function…

Q: B. y = Inx and x - y - 4 = 0.

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Q: Q5: If f(x,y) = 6x , g(x, y) = x-3y find Vf,Vg,V(fg) %3D

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: Q1 / Find x, y, and z 3x [ 2х — 1 6 ] = [; ?] 2 x + 2y 2

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