If 1 =- V(x2 + y²) [(xyz – 3xy)a, + (zy² + 3x² )a, + xy az] And B = r² a, + sin 0 aø Find JÃ x B| at P (1,2,4)

Q: f= x? + क) | + ला (i) of =? (üi, af मु] liv) of

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Q: Find all harmonic conjugates of u(x, y) = x³ - 3xy² + 2y.

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Q: (D² - 4D + 5)y = e*; y a. y= e²*(C,cos2x + C,sin2x) – –e 10 b. y e2*(C,cosx + C,sinx) +e 10 C. y =…

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Q: 2. By hand, sketch the following against independent variable t: a) x₁(t) = Re(2e(-1+j2m)t) b) x₂(t)…

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Q: If f(x, y) = sin(xy+, then fy(0, 1) = X+x3 5 undefined 2 1

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Q: (1) Let f be a differentiable and μ-strongly-convex function whose minimum is achieved at x*. Let us…

A: To solve this problem, we need to analyze each statement and provide the corresponding solution. 1.…

Q: Let F = cos(4t) i + 3tj+ 4t°k and G = t cos(4t) i + t j+4e#k Find the cross product F x G =

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Q: c) 4y? — 7у — 12 dy У(у + 2)(у — 3)

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Q: for Q4\ Find fo dx 1) y = (x cot 2x) 2)x+4x√√y-5-3

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Q: If flix.y)=XSin²(y)+y°Cos(x) prove that fn=2[Costy).Sin(y) ySin(x)]

A: First of all, we partially differentiate function f wrt. x and then we partially differentiate the…

Q: b) Find all the analytic functions for which Rez = Im f(z)

A: b) A function f(z) is said to be an analytic function at any point z=a if f(z) is differentiable not…

Q: 2) x + xy+y -7= 0, (1,2) Ans. -4/5

A: We have, X^2 + xy + y^2 - 7 = 0 Differentiate with respect to x, we get 2x + [ x • dy/dx + y • dx/dx…

Q: Find the general solution of the system of equations 2 -5 x' 0 = - ( ² = ₂ ) x + ( cost), 0 < t < *.…

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Q: Q1/ If z = f(x, y) and z* - y? = 6x²y°z7 Find: and dz

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Q: If x²y" + xy' + (x² – ÷)y=o x >0 ,V,=x 2 sinx , and y =y;v. Which of the following equations…

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Q: Use Cramer's rule to solve for y (y only) in x+y=z=6 3x - 2y+z=-5 x + 3y - 2z = 14

A: The given system of linear equations, x+y-z=63x-2y+z=-5x+3y-2z=14 We have to find the value of y…

Q: Let sin(4x + 7y°) x3 + y5 if (x, y) # (0,0) f(x, y) = 0. if (x, y) = (0,0) %3D Which of the…

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Q: 16. Find the values of r so that the function y= e™ satisfies the equation y" – 4y' – 21y = 0. A)…

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Q: ex 3-4e2x 21) f dx

A: Given expression:  ∫ex3-4e2xdx

Q: (D² – 2D- 3)y = 2sin x a. y, = -cosx – 2 sinx =csx COSX b. y, = --cosx - - sinx COSX c. Y; = - cosx…

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Q: 1 = x²y" + xy' + cx? - +»v=o x>0 ,V1=X sinx , and y =y,v. Which of the following quations satisfied…

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Q: Q NO3)IF y=Jsinx + Vsinx + Vsinx + . then show that(2y-1) = cosx .And Also Find dx (5vcosx) dx

A: Our objective is to find the derivative of above functions.

Q: Use the method of Characteristic to solve U t tuux = 2t, u(x, 0) = 3x.

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Q: Suppose that 4x² + 2y² = t² and y=tsin 0. Find ду (27) ət 0 and at ?x

A: The given equation is y=t sin θ. Consider sin θ is a constant term.

Q: dy Find as for y = x - x sinx O 1) - 1 - 3x² cosx - x³ dy sinx dy O 2) = 1 - 3x² sinx - x³ cosx °…

A: Differential

Q: Q2- If Z = f(x, y) = sin(x³y5) Find fyy and fyx

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Q: -1

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Q: 4. Find d?y/dx² for the following functions: a) y = sin x? cos 2x b) y = cos (sec2 3x) c) y = x²(x³…

A: Since you have asked multiple questions, we are answering the first question for you as of now. If…

Q: Differentiate. 1) f(x) = 4x2 - 5x+4 A) f'(x) = 4x-5 2) y = (2x² + 3x)² A) B) f'(x) = 4x²-5 = 8x3 +…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: What is the image of (4,-1)(4,−1) after a reflection over the line y=xy=x?

A: Reflection over y=x means:  (x,y)→(y,x)  We need to find reflection of (4,-1) over y=x line .