b) Eiven that x -t'+ 3t² and y=tt- 8t? 2. Find dy i) Find when t=1 dz

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A: dsdt=s+et  It can be solve by integrating factor method I.F =e∫1dt =et solution of DE is…

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Q: dz Find when u= 0, v= 1 if z= sin(xy) + ysin(x), x = uv, y3Du² +v?. du

A: Given  z = sin(xy) +ysin(x)              x = uv and y = u2 + v2  Substituting x and y in z we have…

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A: Given      If    f(u,v) = tan-1(u/v)    u = x cosy    v = x siny

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Q: Evaluate the line integral / (7x + 3y)dx + (2x – 8y)dy along the curve C: x = 8 cos t, y = 16 sin t…

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Q: Q2\ Shoe that another from of Euler- * Lagrange equation is : L, -L,½ -y'L,ý - y"L,51 = 0 . - y 'Ly5…

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Q: 4) Solve the followingIVPusing LaplaceTransform. y′′−6y′+15y=2sin(3t)    ,y(0)=−1,y′(0)=−4

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Q: Evaluate the line integral / (2x + 4y)dx + (2x – 9y)dy along the curve C : x = 4 cos t, y = 8 sin t…

A: Solution is given below:

Q: (b) Calculate fe" con(r2) dz using integration by parts as many times as necessary.

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Q: 4. Evaluate 3x?ev° dx + 2x°ye° dy where the open curve C is the semicircle x² + y² direction. 5, y >…

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Q: A point moves along the intersection of the elliptic paraboloid z = x + 3y² and the plane y = 3. At…

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Q: Compute yarctar y? = 1 – 1+ y? ctan(y)dy. Hint: Note that 1+ y? fractan(g)dy- +C

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Q: What is the value of the line integral ∫ AB y dx + x dy, if x = 3*t, y = 4*t + 4 and 0 ≤ t ≤ 1?

A: I am solving this in step 2

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Q: dy Exercise: find O If y= Vu ua Sinx y= -Secu %3D

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Q: Consider the curve C parametrized byx = −1 + 6 sin t and y =(1/2)− 6 cos t for −π ≤ t ≤ 7π. What is…

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Q: Evnlunte: (а) (- xy) dydx (b) dr(x-) dy, where y, = Va? - x?

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Q: 3 Consider cune detined by y cos (T2) =UY +y+2 2 ) Verify point (2,-2) belongs to this curve, fond…

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Q: 4. Given YZ tangent to oJ at point Y and m<WYZ = 104, %3D what is the measure of WXY?

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Q: 4. Find the length of the arc C = {(x, y): y = V16 – x²?,0 < x < 3}.

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Q: 5. plot x?-y?=z (Elliptic paraboloid) in 3D.

A: Note: According to bartleby we have to answer only first question please upload the question…

Q: c. Based on the orientation of your rectangle would we integrate with respect to x or y? С.

A: Follow the procedure given below.

Q: Find in terms of x and y if arctan(r + x²y) = ry

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Q: (iii) dz< 22 + 2 where here y parametrises the straight line segment from 0 to 1- i.

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Q: au +20 dy 10 www ax dy dy?

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Q: (a) Obtain the equation of the tangent plane and the condition for tangency to the conicoid Ar? +…

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Q: Evaluate fc 2x ds, where consists of the arc of the parabola y= x2 from to followed by the vertical…

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Q: Evaluate the line integral | (x + 3y + 2)ds, where Cis the line segment joining the origin with the…

A: Solve integral.

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Q: Assume that a body moving with velocity v encounters resistance of the form dv/dt = -kv3/2. Show…

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Q: A point moves along the intersection of the elliptic paraboloid z = 2x? + 7y² and the planex = 4. At…

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Q: Compute 2z dz (2² – i)3 when y is any arc z = z(t) in C with |z(t)| > 2 for every t, with…

A: Let the required arc be ABC, which starts at z=3 and ends at z=2i: The shaded area shows a sector…

Q: Evaluate the line integral (6x + 8y)dx + (3x – 3y)dy along the curve C: x = 4 cos t, y = 8 sint…

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Q: What is the integrating foc tor of the equation %3B

A: Topic:- differential equations

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Q: Evaluate the line integral 3xy ds where Cis line Segment Joining (-5,7) to (3,1) the

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A: We will use the approach of the method you mentioned.

Q: TQand TR are secants from Point T to Cirlce A as shown below: s. If mQR = 70° and mSP 34°, what is…

A: Given: To explain the correct of the given statement as follows,