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

Q: 1. Find the orthogonal trajectories of the family of curves x? + y2 = cy.

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Q: 23. Evaluate Jcxy dx + (x + y) dy along the curve y = x² from (-1, 1) to (2, 4).

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Q: Evaluate the integrals

A: To evaluate the integral I=∫0π/4∫0ln sec v∫-∞2t ex dx dt dv   tvx - space

Q: Bounded by the curve y = (x + 3)², the x axis, and the lines x =-3 and x= 0. %3D

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Q: 7-The tangent of the curve x^2+y^2- 2xy3D0 at the point (1,1), is * O a. y=2-x. O b. y=x-2. C.…

A: We find equation of tangent to the curve

Q: Find the orthogonal trajectories to the family of curves: x² = C-v'(ln y² –1).

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Q: Find y' for y = vTy at the point (9,1).

A: Given: y=xy ⇒y=x12y12 ⇒y12=x12

Q: Use the composite trapezoidal rule to find approximations to I = (t- cost) dt with n= 1, 2, 4, and…

A: The composite trapezoid rule: ∫abf(x)dx=h2f(a)+2∑i=1n-1fxi+f(b), where h=b-an,xi=a+ih,i=0,...,n The…

Q: Expand x'y + 3y - 4 about the point (1, -2) by Taylor' s theorem.

A: Let, the given function be fx,y=x2y+3y-4 and the given point is 1,-2

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: 2. Show that P(1-x)° dx= x'(1-x) dx. %3D 0/

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Q: Z=8x+12y subject to 4x+6y>14 , 4x+5y > 9, x20, y20 x=? (2 decimal places) Minimize

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Q: Find S (x + In y) dydx

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Q: Evaluate (2x-y)dx+(x+3y)dy along the path C: curve on y = 1-x² from (0,1) to (1,0).

A: Given the line integralI=∫C(2x−y)dx+(x+3y)dyCurve y=1−x2

Q: 8) Find the family Coff esponding to of orthogonal trajectories y=kx".

A: To find the orthogonal trajectories corresponding to below curve.

Q: : )-+(÷), zw= (C) dx 1 et %3D dt 1 (: :)-+(-), -= (C) dx dt 1

A: Given dxdt=0110 x +ete-t Here let take A= 0110A-λI=-λ11-λ=0λ2-1=0λ=±1 Hence the eigen vector for 1…

Q: first and second derrivative of: y=Arccos(e^2x)

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Q: 7. what is the durivative oF q= arc cSc V1-3X %3D 3 Cz -Gx)I- 7 X 3. C2-6x)1-3x (-3x)-3x 3 C1- 3x)-3

A: First make it in simple trigonometric functions then diffrenciate it and just put all the given…

Q: (6) Find the orthogonal trajectories of the family of curves r= 2C cos 0, where C being parameter.

A: Consider the given curve. r=2Ccosθ          (1) Find the derivative of the given equation.…

Q: 13. Show that the length of the portion of any tangent line to the ball x2/3 + y2/3 cut off by the…

A: Given: The equation of the ball is: x23+y23=a23...........(1) We have to show that the length of the…

Q: The value of the line integral fydx + xydy over the straight-line path C from (0, 0) to (1, 2)…

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Q: 」enr一2) dz csc (4r – z) dz dz dz 17. 2 V1 – sen 2z V1 – cos (4- – 2z) In | csc (4- – z) – cot (†7 –…

A: Integrate as general

Q: Find the particular soluti y' + 3x²y = 3x² %3D Initial Condition: y = 6 %3D

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Q: Find equations for the lines tangent and normal to the cissoid of Diocles y (4 – x) = 9x° at (2,6).

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Q: Consider the inmplicitly defined curve xy +3x2 4. %3D O Verify that the point (1, 1) is on the…

A: Consider, the implicitely defined curve                          xy2+3x2=4 We have to verify the…

Q: What is the minimum value of y = 3 + cos 2x?

A: Please go through the attached solution. I hope that this solution will help you. Thankyou . Best…

Q: Find an equation for the tangent plane to z-x-y = 3 at the point (2, 1, 8) Z - ) %3D

A: given z-x2-y2=3 at point 2,1,8

Q: Show that: 2 2 4: +2} | sin 2y x=1 y=vx TOX dydx = 2y dydx+ _3 x=2_y=vX

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Q: The Normal line at the point (0, –1, 1) to the 3 surface exy - xy² + z³ = -2 is 7=y+1=² Select one:…

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Q: Evaluate the line integral Sc (2x² − 3y) dx + xy dy, where the curve/path C is the line 3 y = 2/2 x…

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Q: The

A: Below is sketch of  the given function.    Rotation about x axis will give a volume in 3D plane.

Q: Find the tangent plane to the graph of **yz +z'e* -y² = 5 at (1,3,2).

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Q: If the equation of the tangent plane to x2+y²-83z2=0 at (1,1,/2/83) is x+ay+Bz+y=0, then a+ß+y=

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Q: A rectangular plate with an area of 36 cm? is to be produced on a lathe in such a way that the…

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Q: Evaluate aned on c indicatid curve 2. 2. y+ Y( sm3x +ca 32,22 3t ,4=t,0zt2|

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Q: If Z = x + iy than Z is: Z = x - iy Z = -x + iy Option 3 Option 2 Z = x + iy Z = -x - iy Option 4…

A: Explanation of the answer is as follows

Q: Obtain the particular solution for: 2y" +2y=2sinx y(0)=0, y'(0) =1 By using method of variation…

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Q: Find valume bounded by abave Z:4-20 and below by Z-xy 2.

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Q: Solve for y + In lyl at x=6: y'=(yx^2-y)/(y+1); y(3) = -1 4.5

A: The given differential equation is y' = y x2 - yy +1  with initial condition y ( 3 ) = -1. To solve…

Q: #2. Show that the line integral (sin y dx + (x cos y – sin y) dy)

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Q: Calculate the curve integral ∫c ( 3x2 - 3yz + 2xz )dx + ( 3y2 - 3xz +z2 )dy + ( 3z2 - 3xy + x2 +2yz…

A: Using green's theorem to find the line integral.

Q: 3z2+x 30. If z – xz – y = 0, prove that- =- ax dy (3z²–x)³*

A: Let's find.

Q: Find Ja xydx + sin(x)ydy, where C is the boundary of the triangle with vertices (0,0), (0, 1) and…

A: Let I is the value of given Line Integral.

Q: Show that the surfaces S1 : 4x + y° + 9z² = 108 and S2 : xyz = 36 are tangent at the point (3, 6,…

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Q: Find the minimum and maximum values of y = V120 - V6 sec e on the interval [0, ] fmin fmax

A: Solve

Q: 3. Find general Golution y" + y= Secx

A: Given that, find the general solution y''+y=sec3x (D2 +1)y=sec3x

Q: OFind the aquahon of the Hangent to the at point Lircle X2 +8Xt PCI,3)

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: The minimum value of n required to approximate xe dx by composite Trapezoidal rule with an error…

A: Find the minimum value of n required to approximate ∫02xe-xdx by composite Trapezoidal rule with and…

Q: 10. Find a tangent plane to z² – x² +y² = 1 at (7, –5, 5).

A: To find a tangent plane to the given curve at the point (7,-5,5)

Q: 19. Sobve (1-x*)-+m*y=0 dy=m dx where x=0, y=0,

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