S6xw, fx,w (x, w) = 0, 0sxs 1,0 < w s Vã otherwise (3x2, fx(x) = lo, 0

Q: A continuous tunction y=f(x) is known to be negative atx=2 and positive at x=6. Why does the…

A: A continuous function y=f(x) Given :f(x) is negative at x=2  and f(x) is positive at x=6 We know…

Q: 1.If f(x,y) cos(4x-2y)+ln(y² -2x) find £xy fx fxy,

A:

Q: 2 X+y +Z=lo Gouss eleminahin 3 X+ 2Y4 32=18 X +uy+ 9Z= 16 ماركة العرض من قبال

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Q: f(x, y) = /2x – y /2х — у f(x, y) = In(9 – x² – 9y²) f(x, y) = /1 – x²? - VI – y² S(x, y) = Vy + /25…

A:

Q: 6. For the function f(x,y) = 8x³ – 12xy + y3 a) Find all critical points of f (x, y)

A: Solve all the three parts for the given function f(x, y)

Q: 4. f(x, y) = 10x²y* – 6xy2 + 10x2; fx(x, y), fy(x, y) %3D -

A: Consider the given function as fx,y=10x2y4-6xy2+10x2

Q: (b) lim (z.y)→(0,0) Vr4 + y3 +1–1

A: limit of the rational function

Q: Vx? + yZ 49x2 49 [F,(x, y)]² + [f,(x, y)]² 1+ x² + y2 e have [f,(x, y)]² + [f,(x, y)]² = /

A: This is the question from vector calculus.

Q: (2xy+ 3x2)e, +(x² – 2yz + 2y)e,- (e2 + y?)e, olan f(x, y, z)

A: Given that the function is

Q: Find L(x). 2y x 3t %3D y + a' = 3e-t x (0) = y (0) = 0 3s2 L (x) = - (s+1)(s-2)(s²+1) 3(s-1) L (x) =…

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Q: du -xy du Ifu =f(x² +2yz,y² +2zx) Prove that (y- zx)-(x² - yz) -NX ду

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Q: xyz 3. If f(x, y,z)= In| +e 2 find f,, f, and f..

A:

Q: 1. If f(x, y)=3x' cos y– y sin x– 2.x In y- yln x-4x²y, find ôf ôf d²ƒ _ô²ƒ

A: According to question given thatf(x,y)=3x3 cosy-y2 sinx-2x ln(y)-y ln(x)-4x2y

Q: 37. f(x,y) = 9-x² – 7y³; f.(3, 1), fy(3, 1)

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: 21. Find div(F), where F(x, y, z) = xyzªi+x²zªj +4x²yz³k. a) -4xyz³+xz4 b) x²y+xz4 c) yz + 3x²yz² d)…

A: Topic = Algebra Correct option = d

Q: 2x – 5y (1, y) # (10, 4) Find C so that the function f(x, y) = V2r – 5y +4 – 2 C (x, y) = (10, 4) is…

A: Given function is fx,y=2x−5y2x−5y+4−2, x,y≠10,4C                        , x,y=10,4 Given function…

Q: If f (x, y) = Vr³ + y³ In(x² + y²)e*in (zy+y') + x³y+ 10 , then f. (1,0) =

A: A scalar function f(x,y) is a rule that is used to associate a number or quantity with a particular…

Q: 25. For y = f(x) = x2 - 3, x = 5, and Ax = 0.1, find Ay and f'(x) Ax. %3D

A: Given: fx=x2-3 ,x=5 and ∆x=0.1

Q: I. Use the limit of the rates as Ax approaches zero. Ar 1. y = Ax + B 2. y = 2x2 – 3x +5 3. y = x3

A: "Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: If f (x, y) = V3+ y³ In (x² + y³)ešin(zy+y*) + x² + 10y.then fz (1,0) = %3D

A: We need to differentiate the given function partially w.r.t x. The given function is: f(x,y)=x3+y33…

Q: (1) E(x, -x)² =Ex} – nx² | (ii) E(x, –x)(y; -y)=Lx,y, – nxy (üi) E(x, – x)(y, – F) =Ex,(v, - )

A:

Q: x = 2 - t, y = 1 + t, z = 3t; x - y + 2z = (x, y, z) =

A:

Q: 7. f (1, y) = z + y subject to z² – zy + y² = 1

A: Let h(x, y)=x2-xy+y2. Then we have ∇h(x, y) = (2x-y, 2y-x) and we also have ∇f(x, y)=(1, 1). Let the…

Q: Maximize f(x, y) = 3xy Зху subject to x + y = 1

A:

Q: 3y +5xy + 2x lim (1) (z3-2) 3y +2.xy 4(x*-y*) (i) lim (10 x -y +1-1 lim (1.)-0.0) (Hint: use…

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Q: Y : k=0 y' + (2x + 1)y = 0, rrence relation. For k > 0,

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Q: S (x+Sy+wz ) dzoly dz 2 3x X-つ

A:

Q: 5x - 5y2 lim (z.y) (0,0) 7z+7y () Limit DNE 0. O 5/7 O 5/7

A:

Q: if the function u= ln (x^3+x^2y-y^3/x-y) then x su/sx + y su/sy is

A:

Q: 2Fs1 ² f (x, y) dx² proof. (H-w-) 2 ./ = P√= f (gy) - P²Fs (Psy) ар(х,у) 0 as x If f (x,y) → 2

A: Introduction: A Fourier transform (FT) is a mathematical transformation that decomposes capabilities…

Q: dy + 2xy = f(x), y(0) = 4, where xp Sx, 0sx<< 1 f(x) lo, x 2 1 0 < x< 1 y = x 2 1

A:

Q: If f(x) = 1-x* , then an antiderivative F(x) could be Inx| -x А. 6-x C. 5x 3x 5 Inx| – x* 1+x° В. D.…

A: f(x) = 1-x5xAntiderivative F(x) = ∫ 1-x5xdx∫ 1-x5xdx= ∫1x-x4dx= ∫1xdx - ∫x4dx= ln x - x55 +…

Q: 2. f(x,y) = x5 In(y)

A: Given function is fx,y=x5lny. To find the first and second order partial derivative of the given…

Q: x-4y lim (x, y)-(0,0) 6y+7x 3 A O 7 .BO 0.c O does not exist. .D O H/7

A: The limit exists only if the value of the limit taken along any path is equal to a fixed value.

Q: maximize f(x,y)=xy subject to the contraint 6x+y=18  the last question is what is the maximum valye…

A: max . fx,y=xyS.t 6x+y = 18     6x+y=18⇒ 6x+y-18=0∴ gx,y=6x+y-18=0    Fx,y,L=fx,y-L g x,y⇒…

Q: dz Find in the function xyz + 5xy = x² + y? + z? dy 2x – yz – x2 dy A. dz - - xy – 2z В. dz 2x – yz…

A:

Q: Find fy if f(x, y, z)=1-2xy²z+x²y yxy B) -4z O A) 4z O C) -4 O

A: Sol

Q: Find minimum and maximum for the function 6 x + 4 y under conditions: x2 0; yz 0; -x+y s 12; x+ys…

A: The objective is to find maximum and minimum value of the function 6x+4y.

Q: 48xyz < (3x + 2y)(y+ z)(3x + 2z) for every x, y, z E [0, +∞[.

A:

Q: (c) Suppose that two of the pipes become blocked so that x3 = 0 and x1 = 0. Determine the flow rates…

A: Topic - flow diagram

Q: Find fzyx If f (x, y, z) = ln(x2 + z) + y2exz

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Q: 3 9-r22 1 dy dz dr 9-r2 0_æ²_22 (x² + y² + z²)1/2

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Q: Find all the local maxima, local minima, and saddle points of the functions in Exercises 11-20.

A: (10)Consider the provided function, fx,y=x2+2xy Find all the local maxima, local minima, and saddle…

Q: If y(x) is a solution of y' = (y+1)(50 – y) with y(0) = 0, what is the limit of y(x) as x approaches…

A: Given: yx is a solution of y'=y+150-y. Also, y0=0. To find the limit of yx as x→+∞. As, y'=y+150-y.…

Q: Find f(3,4) for f (x, y) = ln(x + Vx² + y²).

A: We have to find out the derivative

Q: 9. If f(x,y) = -cos x+e*y, find Vf(x, y).

A: For the solution follow the next step.

Q: © f(X,y) = x4 + 'onY -10 © w = x*y - 10yZ z³ + 43X – 7tan (4Y)

A: It is partial derivative

Q: ntegrais. I, da, D= {(x.y) 0sxs20sys2% dA, D = x +2 [['e"d4, D={(x,y)| 0s ys 4,0sx<y}

A: Double integration

Q: What is L[y] if y = u3(t) (t- 3)2? %3D L[y] = e3s . - 3 O Lly) = e3s. 2 L[y] = e-3s. 2 O Lly] = e-3s…

A: