Q3) A) If you have three functions: f (x) = x² – x g(x) = 3x – 1 w(x) = x² – 2 So, find gof (x) and fow(x)

Q: Q3) If f(x,y²) = x² + y² + vxy find : af (x²,y) and f(x²y) ax ду

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

Q: 21. Кх, у) 2х -у ys 4x + 6 5 * 4y s 7 2r + ys7 бу X-6y z 10

A: Step-1 f(x,y) = 2x-y            y ≤ 4x+6 ⇒ 4x-y ≥-6            x+4y ≤ 7           2x+y ≤ 7…

Q: I don't understand why w(x,t)= x+(1-x)t^2

A: Given below the detailed solution

Q: If f(x,y,z)=x²y³-y²z³ Then f;= -3y²z2 Jlgn

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Q: 2/3' 2/2, Suppose 3z? + 2y² + z² = 1 and z = g(x, y) > 0. Determine g, ) and gy 2/3' 2/2

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Q: If the equation xy+xz3-234yz=0 defines z implicitly as a function of x and y, then the value of az…

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Q: 7. Differentiate a) f(x) = ev==t and b) h(x)= (5x² – 8r)e**-4". %3D

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Q: 1 max z = 2x, + x2 - x1 + x2 s 1 Xị + x2 s 3 s.t. 2x2 < 4 X1, X2 2 0

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Q: 12. f(x, y) = x' – 2x – y + 4y, P = (1, 2). -

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Q: - a°y°, show that fæy = fyx. 85 Problem - 24: Given f(x, y) =

A: Solve the following

Q: Let f(x, y) = 2x² + 3y2, then (2, 3) is not a critical point of f(x, y). Select one: True False

A: I have calculated the critical point of the given function

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: Suppose the cost per hour incurred in operating a cruise ship is 5a + b^4v^3 dollars per hour, where…

A: Step:-1 Note:-  your cost expression is not clear here as it can be 5a+b4v3   or   5a+b4v3 , So i am…

Q: You will calculate L5 and U5 for the quadratic function y 2² + z + 14 between z = 0 and z = 2. Enter…

A: To solve the following problem

Q: 2.,3 2) Find fx and fy if f(x, y) = 2x²y³ – 3xy² + 2x² + 3y² + 1

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Q: 4- compute dw dw дх' ду at the point (-2,3) if w = (2x + 3y - 1) ²

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Q: The function y== In (3z - 2) satisfies the IVP: (3z – 2)°y" + 9 = 0, y(1) = 0, y'(1) = 8. Select one…

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Q: Xxy-Z = Gauss eleminatin %3D 2X -y42=5 -x +2y+23 or

A: We have to solve given problem:

Q: Suppose that f(z, y) = e-2-2y –2z+y Then the maximum is

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Q: Find the maximum and minimum values of the function f(r, y) = x²y subject to 5æ² + 4y² = 60 Maximum…

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Q: Maximize f=-x-3y subject to -2x+y = 2 X,y >= 0

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Q: (1) If f(x) = { 3 x2 ; -1<x<2, then 0 ; otherwise compute [ xf (x) ]dx and [x²f(x)]dx

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Q: 8. 8 If , f(x-c)dx = 5 where c is a constant, then f (x)dx= -c

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Q: 11. If f(r) = rª and g(r) = r³, then f' (x) = 4x³ and gʻ(x) = 3x². The Chain Rule multiplies…

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Q: 2. (1 point) If § f(x)dx = 12 and f(x)dx = 4 then which of the following statements is FALSE? (A)…

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Q: If (1,1) is a critical point of f(x,y) = x³ – 3x + 3y² – 6y then (1,1) is:

A: (1,1) is the local minimum point   explanation is given in below step

Q: A manufacturing company produces two models of an HDTV per week, x units of model A and y units of…

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Q: What is r' (x) when r(x) = In (x³ + 2x2 + 3x +1)? Select the correct answer below: In (3z2 + 4z + 3)…

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Q: 2.2 11, IfF = xyz\+x*y°z}+ xyz k then find div F at (2, 1, – 3).

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Q: B) fometie w= xty+y2-23, x²ry*+2?=6

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: 3x + 11y af If f(x, y) = then is : 3x – 11y dy - 66x (3x + 11y)² 66x (3x – 11y)² 66x (3x + 11y)2 66x…

A: Partial derivative

Q: 4. y=6-ax-x", y = x+l6, about the a %3D | yaxis

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Q: 2n bị 2n 2n paz x a, , b2 = a, xa x a, , bz = a, x -аз ха,,

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Q: [1] Determine the orthogonal trajectories of y(1+2x²)=ax.

A: The given equation is:y1+2x2=axy=ax1+2x2              ..............(1) Determine the orthogonal…

Q: If 6x³ +x* –y³ 2x² +y² f(x, y)= if (x, y) (0, 0) if (x, y)= (0, 0) then f,(0, 0)= O does not exist

A: Thanks for the question :)And your upvote will be really appreciable ;) Correct option (A) does not…

Q: If y=2x²-4, what is its inverse? or Oy¹--√2 Dy^--, DOIN such that xs-4 such that x2-4 such that x20…

A: Given, y=2x2-4 To find the inverse, we need to swap the variables 'x' &amp; 'y' x=2y2-4 Now solve…

Q: 1) Show that (a) y =xe satisfies the eq. xy' (1-x)y (b) y =xe"A satisfies the eq. xy'=(1-x²)y

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Q: 14I hox)= x)-0, whese fCn=2 and fとい=8,

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Q: - If f(x, y) = cos(2x) − x² e5y + 3y², then fxy = -10x e5y True O False O

A: A detailed solution is given below.

Q: 9 2. If fS(x)dx= 37 and g(x)dx=16, = 16, find [2f(x)+3g(x) ]dx- %3D 0.

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Q: 3 Fivd fy fz fxz if

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Q: A goldsmith finds that the demand for gold is governed by p(x) = –x² + nx, where z is in (troy)…

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Q: 7x + 19y fe is: dy If f(x, y) then 7а — 19у - 266x (7x 19y)2 - 266x (7x + 19y)² 266x (7x – 19y)² -…

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Q: 1) If h(x) = x³ +1, find h-'(x). (A) h-'(x) = 3+ (x +2)³ (B) h-(x) = Vx – 1 (C) h-(x) = 2r³ – 3 (D)…

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Q: (2)If ø = xyz – 2 y²z+x²z?. Find div grad ø at points (2,4,1)

A: Given that        Φ =xyz-2y2z+x2z2  Here we have to find div grad Φ at points (2,4,1).

Q: A x² B --x-In Ix+11+ C x² 2 -x+ In lx+11+ C 5x²=² dx x+1 C x² D x² +x-In Ix+11+ C +x+ In lx+11+ C

A: The given integral,              ∫x2-2x+1dx

Q: (1, if x 2 %3D plot

A: f(x)=1, ifx&lt;01-x2if 0≤x≤2x+1if x&gt;2

Q: If we use the secant method on fx) = x+x+3 with x2 and X-1 = 1, then X, is

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Q: 2 Find / U(x) + 4g(x)]dx if -5 2 2 | f(x)dx = 6 and / g(x)dx = -3. -5 -5 2 [f(x) + 4g(x)]dx = i %3|…

A: Given∫-52f(x)dx=6∫-52g(x)dx=-3

Q: 7 If f(x, y) = (3x³ + 2y² – 30)', then fy is - given by :

A: