x2 If w = x".f then show that: + y², X. Wx + y. wy = nw.

Q: If J_f{x)dx=10 andJ, f{x)dx= 3, then J, f(4 – x)dx=?

A: According to our guidelines we are supposed to do only one question. Kindly repost the other…

Q: Given f(x, y) = x² – 3x?y – y", find fz(r, y) = fy(x, y) = frz(x, y) = fzy(x, y) =|

A:

Q: z = x2 + xy4, x = uv? + w°, y = u + ve" dz when u = 3, v = – 2, w = 0 dv then find:

A: Solve by partial differentiation

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

A:

Q: (c) Given tanh (x) + tanh (y) = 1, show that, dy 1- y? dx 1- x2

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Q: Find where 1)let . V°g r = l7| -- g(r) = In(r³) s = xi + yj + zk * vo x Vp 2) find = yz + zx2, P =…

A: Gradient and cross product

Q: Since fy(x, y) = x², find f(x, y). f(x, y) = + g(y)

A:

Q: f Vf(x, y) = 0, then Duf(x, y) = 0 for all u. %3D %3D

A: True

Q: 2x-y if F(x, y) = xy é e af ар ay ах find

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

Q: Q.1B) If w = f(u,v) where u = tan"12 &v=In(x² + y²), the show that: dw Х- +- дх дw dw <-2- ду ду

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: 03. Find se and *. If f(x,y) = 2e* + Iny² ,and x = 2t + r2, y = ; %3D at r+1

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Q: dy Given that y = 5u+ 4 and x = -u', hence find dx

A:

Q: 16 -Σ(Σ») f(x, y, z) = Σ · (x + y + zn?) 2

A: Given: fx,y,z = ∑n=116∑k=1nk-x+yn+zn22

Q: J f(x)dx = f(x)dx =7, then J f(x)dx = If 4 and

A:

Q: If f(x, y) = x²e + cosy af af then find dy

A: We will use partial derivative to solve this.

Q: dy Find dz If ze" + (Inz)y + y? = 3

A: Find dydx if xex+ (ln x)y +y2 =3 We will differentiate terms and then sum them up. So, ddx(xex) =…

Q: In Exercise, verify that S and T are inverses.

A: GivenS:R2→R2 by Sxy=4x+y3x+yT:R2→R2 by Txy=x-y-3x+4yTo check S  and T are inverse of each other.

Q: ize P= 3z + 4y E to 21 + vS 16 27+ 3y S 24 z20, v 20

A: Introduction: Linear programming is the most basic method for optimizing a problem. We can use this…

Q: 5. Given that f (x, y) = sin y, determine fy(x, y).

A:

Q: Given f(x,y) = ex cos y, Evaluate fx(2,0)

A:

Q: Given f(x, y, z) = V 42? + 6y² + 3z², find fz(x, y, z) = fy(z, y, z) = %D f:(x, y, z) =

A: we need to find out partial derivative of first order

Q: Euler's difFQ 3. (y()) =VZ Eq cal g'ral-2y cx ) =x (y (x )

A: Given differential  equation:-    y' - 2y = xy3        y(1)=2√2

Q: Let f(x, y) = 6e sin(7y) af af dy

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Q: Q1 but f(x,y) = x²y²sin-'O xf, + yfy = 4f (x,y) between

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Q: Q3. Find af and at se If f (x, y) = 2e* + Iny2 ,and x = 2t + r2, y = ar r+1

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Q: 4. If f(x, y)=: Vx² +y? 1 , find f, and f,.

A: Given data is : fx,y=1x2+y2  To find fx and fy

Q: Gy Let Px) = x²/3, x. thens Rx) = x2/3 ×シ。 then: %3D O Find ê cx) ? 2 Gruphs off R and f

A:

Q: Q.1B) If w = f(u,v) where u = tan-12 & v = In(x² + y²), the show that: %3D dw aw aw X +y¬ 2- ax ду…

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Q: If u- f(x) where y=J x+y%*34 show thal do

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Q: 2. For what value(s) of h, y belongs to Span {v1, v2, v3}? Where 5 -3 V2 = -4 V3 ,and y = 3 h

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Q: Find Duf at P. 2 f(x, y, z) = 6x³y°z°; P(2, – 2, 2); u = ;i + -k

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Q: if y³ - y = 2x Then, d'y -24y prove that dx (3y -1) |

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Q: Find fr and fy for f(x,y) = I+y fz = /(r+y)? and fy = /(r+y)2

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Q: MATHER 三 Zxy if f(uv) u-**y ,V Xy.

A:

Q: 11. f (x, y) = ery subject to a? + y? = 16 %3D

A: The objective is to find the lagrangian multipliers for fx,y=e2xy subject to gx,y=x2+y2-16. To solve…

Q: f(x, y) = e&z– 4y af af ду

A:

Q: If z = f(x, y), where x = 2ts and y = t2 + s², show that () - 2 + 2x + 4y %3D dsdt

A: Here given z=fx, y and x=2st, y=s2+t2

Q: Let y = f(x1, x2, w), where x1 = 2w2 and x2 = w+1. Find dy/dw.

A:

Q: Find vf(x, y) if f(x,y) = e* c cos y 5.

A: Note : according to our guidelines we can answer only first question because there are multiple…

Q: if y' - y =2x Then, d'y -24y prove that dx (3y –1)

A: Given that: y3-y=2x

Q: Find . for (x,y) = x² + y² af af ду' дх Find ду' дх Je Je for f(x,y) : sin xy? x2+1

A:

Q: af when s = 1,t = 1 for f (x, y) = x³ – 3xy - 6x + 6y ,x = 2t + s, y = 2s – t. a) Find as

A:

Q: 2: find fr, fy, and fz. 9 f(x, y, z) = 1 + xy? - 222 5 f(x, y, z) = x - Vy² + z?

A: (a) Given f(x, y, z) = 1 + xy2 - 2z2 So fx = ddx(1 + xy2 - 2z2)    = ddx(1) + ddx(xy2) - ddx(2z2)…

Q: If f(z,9) dz dy = K. where K is a constant, then 21 f(z, y) dy dz |3D

A: Given,          ∫ab∫cdfx,ydxdy=K , where Kis a constant , then ∫cd∫ab21fx,ydydx

Q: If z'y +y = r dy 1, then at (0,-1) is

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: f (x, y, z) = xªe²y+æ² zy? – 5zæy³ | af af af dx ' dy' dz Determine

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Q: Find Vf(x, y) if f(x,y) = e** cos y ..... ...

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Q: Use the linear approximation to ƒ(x, y) 12x² at (3, 9) to estimate f(3.1, 8.8). y2+7 (Use decimal…

A:

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.