Let C₁ be a straight line in the Argand plane from (0, 0) to (3, 3), and let C₂ be the path consisting of a straight line from (0, 0) to (3, 0) followed by a straight line from (3, 0) to (3, 3). Calculate the following integrals directly: i. [zºdz ii. [ z dz C₂

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Q: Use these equations to find ∂z/∂x and ∂z/∂y for the following. x9 + y7 + z3 = 4xyz

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Q: nd the tangent plane to the equation z = a? – 4y? – 2y at the point ( – 3, 3, – 33)

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Q: 2. Find the points of contact of the two tangents to the curve, 6y=2x³+9x³-12x+2, parallel to the…

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Q: 8) Given z =f (x.y) =1- (x² +4y2) ,Find : a)The vector function, 10 normal to the surface of f at…

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Q: Calculate the rectangular approximations R1, R2, and R4 for f(x)=2x−1 over the interval [1,5].

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Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In V x2 + y², (6,…

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Q: Determine Du f{8,1.3) for f(x,y) = 4x?y + 2xy in direction of v = (-1,1).

A: Suppose f is two variables function of  x and y  .Then direction derivative of f at any point in…