а. f(c) 3D Vс + 20 b. g(c) 3D Vс+ 20 — 1 c. h(c) Ус + 20 — 1

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: f(æ, y, z) = æ²y+ 2y²z+ 3æz?. Compute fa: (1, 1, 1). None of these. 3

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Q: af If f(x, y) 3x+7y (3x-7y) then is given by: 42y (3x–7y)² 21y (3x–7y)² 42y (3x-7y)2 21y (3x-7y)² -

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Q: Use Cramer's rule to fins a solution: 3x-2y=4 6x-4y=0

A: Cramer’s rule:

Q: Use Cramer’s Rule to solve…

A: The solution is given as

Q: 25n Evaluating sec will yield to 6 V3 A 2 2/3 B 3/3 © - 2 V3 D 2.

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Q: y2 2p Thus |g1|+ |92|+ Iaml 3p 0, ((V4p +1-1) (V+1- 2) <0. 1) (vp+1-2) <

A: as given q1+q2+...+qm=3py2 also py2=2p+1-4p+12p              ...i thus, as we know…

Q: 11 - If f(x) = Vx + Vx then f'(1) = ? %3D a) o V2 b) O 4V2 3. c) 4V2 3. d) 2/2 Boş bırak

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

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Q: (b) If V'u =0 for x2 0 and if u f(y) on x=0, Show that ,y): +(y-5)

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Q: if y = secx prove that y^2+y=2y^3

A: Equation relates the number of variables combined together by algebraic entities using equality…

Q: If y(x) satisfies y′′(x)=y′(x)(1−y′(x)),y′(0)=1/3,y(0)=1, then y(x)=?

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Q: 1.) Evaluate: S(2 + y²)²dy

A: We have to find integral

Q: Determine whether X and Y are independent: 2e--2y x, y > 0 a. fxy(x, y) =

A: Hello! As you have posted 2 different questions, we are answering the first question (4-2). In case…

Q: Compute f, aL a2f and :f(x, y) = (x + y)(2x + y)² ax' ay дхду

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Q: If f(x, y) 3x+7y af then is given by: (3x–7y) 21y (За — 7у)? 21y (3x–7y)² - 42y (За — 7у)2 42y…

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Q: 1. Find x, y, and z so that x + y 4x 2y -16 -- y 11 4 Z

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Q: T: R2 R2 is defined by х + 7х, [3x, – 4x2] X1 %3D and B = {u,,u,} and B' = {v,v,}, where %3D -- --…

A: Given transformation T:R2→R2, defined by Tx1x2=x1+7x23x1-4x2 and B=u1, u2 and B'=v1,v2 Here u1=22,…

Q: for w = ze(zy²+2:). Do not include =" in your answer.

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Q: Show and use d(Xn, FCN))<« d(Xn-1 'x) Vny? To prove X = fx) %3D

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Q: 4,5 f (x,V)= Sx"y%,compute fx and fy

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Q: - If y = e3x and y = e-3x , prove that: - %3D d²y 9y = 0 dx2

A: Given: y=e3x⇒dydx=ddxe3x⇒dydx=3e3xNow,d2ydx2=ddxdydx       =ddx3e3x       =3ddxe3x       =33e3x…

Q: 9x + 2y + 4z = 20, x + 10y + 4z 6, 2x-4y + 10z =-15 54x +y+z = 110, 2x + 15y + 6z = 72, -x + 6y +…

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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: Q2: Consider the IVP: y=1+2,1sıs2, y(1)=2.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 2. A counterexample can be used in all of the following situations except?

A: A counterexample is a particular case that demonstrates the falseness of a general argument.

Q: 3. Show that S4 has the presentation (x, y|x* = y² = (xy) = 1). %3D

A: To show: S4 has the presentation x,y| x4=y2=(xy)3=1

Q: Show that A Yk= V' Yk+r

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Q: 9. If y = V-|x|, then Dr = %3D %3D

A: Df :  Domain of function f  The set of all input values where f defined

Q: Solve for x, where u = (1, −1, 2), v = (0, 2, 3), and w = (0, 1, 1). 2x − u + 3v + w = 0

A: Given u = (1, −1, 2), v = (0, 2, 3), and w = (0, 1, 1). And 2x-u+3v+w=0 Plugging the values,…

Q: If x + y + z = 12 & x² + y² + z² = 96 & !.!,!= 36 then value -+-+ -%3D X y of x³ + y3 + z³ is

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Q: 15. У eaw 17. f(w) = %3D w2 + w + 1 19. y= el+vã Vn

A: As asked we can find solution to question no-17 and 19 as below

Q: 8. Show that jxk i.jxk (а) і— kxi (b) j= i.jxk ixj (c) k =- i.jxk

A: Topic = Vector

Q: ở =, then If f(x, y, z) = In(2 + x² – 2y² – 3z), Duf(2, –1, 1) = A) % 11 V3 В) 11 C) D) - E) OC O D…

A: The solution is given as

Q: Q: If u =f(x² +2yz, y² + 2=x)Prove that (y-ax

A: Step by step compute the derivative with respect to each variable x,y or z. Then substitute it in…

Q: 2s f( 8ts“, ), (x, 9) = 7xy, and af af ;(x, y) : Assume that w= Find and ds %3|

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Q: Prove if X,Z, y > 0 xy (3x +2y – 4z)+ yz(y+3z – 4x)+ xz(x+2z –- 4y)>0 then

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Q: Additional Problem Prove the statement: 3X CZ such that Vx E X, 2 | x and 3 | x.

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Q: 19. f(x, y, z) = x² + y² + 2², holds 2x + y + z = 1, -x + 2y3z = 4

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Q: Q3) If f (x, y²) = x² + y² + Vxy find : af(x²y) %3D and (x2y) ax ду

A: This question is based on Partial differentiation.

Q: If f(x) = 12sin(green wave), then the red wave isni %3D 20 |-31/2 |-T1/2 T/2 3h/2 2n 5T -10

A: Solution A sinusoidal wave can be represented as f(x)=Asin(2πfx+P)..........(1) Where A is amplitude…

Q: 4. Now, determine the value of c in (0,1) such that f'(c) = 2 %3D fx) =4x

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Q: Suppose T(x,y) = (2x, 2y) and U(x,y) = (x, -y). Is T∘U=U∘T?  Justify your answer.

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Q: Given that z = f (u,v), u=x + y and v = 2x - 2y. Show that 4. дхду ди?

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Q: Evaluate /, a Te dydx y2 2 JJ4X-x² 32 dydx (x²+y²)' V4x-x? O 4 In(v2 – 1) – 4+7y/2 3 4 In(v2 + 1) –…

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Q: c. St VE² + 2 dt In: Inx d.

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Q: A- If y = e3x and y = e-3x , prove that: - d²y - 9y = 0 - dx2

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Q: g) Suppose y² + [S(z)]² = 2, then (7,1)

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Q: Let f(x, y) = x² + y2 + 2x + 4 and P,(-1,0) then Vfle, is i – j. True False

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Q: If f(x, y, z) = In(2 + x² – 2y² – 3z), 7 =, then Duf(2, –1, 1) = - A) * V3 B) 11 C) V3 D) E)

A: The given function is:    f(x,y,z)=ln2+x2-2y2-3z