2. Find an equation for the plane tangent to the surface 3x2 - 4xy+ z2 = 0 at the point (1, 1, 1). dz ,x = t2 - 1, and y = 3t + 2. Find using the chain rule. dt 3. Let z =

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A: Let's find.

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A: According to chain rule of differentiation . According to power rule of differentiation .

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A: Given the Integral : ∮c(x+2y)dx-(y-2x)dy ⇒Let I=∫C(x+2y,y-2x).(dx,dy) , x=4cosθ and y=3sinθ…

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

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A: We can use concept of critical points in order to solve the given problem.

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Q: Find a parametrization c(t) of the line y = 5 − 2x such thatc(0) = (2, 1).

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A: As per our guidelines,only one question can be solved, Solution for B is given below:

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Q: Evaluate the line integral. { 4) ( y2 dx + x dy; C is the curve x =t2 - 1, y = 4t, 0 st s 1

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Q: (a) Find a function f(x, y, z) which satisfies Vf = (y + 2z, æ + 3z, 2x + 3y) (b) If C' is the curve…

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Q: 1. If F(x, y) = (3+2xy)i + (x² – 3y²)j. Evaluate F. dr, where C is the curve given by r(t) = e'…

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Q: e the line integral Sc(3x?y+2)dx+ (x+3)dy where C is the curve r(t) = (t2, 3+t²) with 0 <t < 1.

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Q: Consider the following. Z = =DVx²+ y?, 5x - 2y + 3z = 22, (3, 4, 5) (a) Find symmetric equations of…

A: a) Here, f(x,y,z)≡x2+y2-z2=0g(x,y,z)≡5x-2y+3z=22P≡(3,4,5)

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Q: 2. If F(x, y, z) = y²i+(2xy+e3=)j+3ye³=k. Evaluate F·Î ds, where C is the curve represented by r(t)…

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