14. Calculate h(r) dr where h(x, y) = (6xy — y³)i + (4y+3x² − 3xy³)j and C' is the curve consisting of the line segment from (0, 0) to (2, 4) and the parabola y=x² from (2, 4) to (3,9).

Q: 2. a). Find the velocity and acceleration of a particle whose position function is x(t)=…

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A: For a function z=fx,y, the tangent plane at point x0,y0 is defined as:…

Q: 6. Find the mass of the solid bounded above by the surface z = y and below by the xy-plane, but only…

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Q: b) Evaluate S(2y + 4z)dx + (2æ + 3z)dy + (4x + 3y)dz, where C is the curve given by r(t) = for 0 <t…

A: given ∫C2y+4zdx+2x+3zdy+4x+3ydz where C is the curve given by rt=t3,2sinπt2,3cosπt2 for 0≤t≤1…

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Q: Compute f cos(Tæ) dæ + 10xy dy, where y is a part of parabola y = 3x? from the point (0,0) to the…

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Q: 1. Find all points on the graph of h(x, y) = plane is horizontal. 3x²9x + 4 + 2y³ - 12y where the…

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Q: 1. Parametrize the curve-segment C(t) of the parabola y = x² from (1, 1) to (2,4) then find [x² dx +…

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Q: Consider the tangent line to the curve r(t) = t2i −(1/(t + 1))j +(4 − t2)k at the point P(4, 1, 0).…

A: Given the tangent line to the curve r→t=t2i^−1t+1j^+4−t2k^  at the point P4,1,0. We have to…

Q: 2. Consider the equation r = 4 – y². (a) Find a parameterization of the segment of this parabola…

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Q: 4. Find the equation of the tangent plane at the point (-2, 1, -3) to the ellipsoid 22 + y? + = 3 4

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Q: Suppose ƒ(x, y, z) = ln(5x² + 6y + 5z²). Find an equation for the level surface of f that passes…

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Q: Explain why a cubic Bézier curve is completely determined by x(0), x (0), х(1), and x'(1).

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Q: Sketch the bifurcation diagram for y = (A– 4t)y (where A is a parameter, as usual). 2

A: To find- Sketch the bifurcation diagram for y' = λ - 4t2y (where λ is a parameter, as usual)

Q: Find the equation of normal to the hyperbola        x2 -9y2=7 At the point (4,1).

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Q: Find an equation (x(t), y(t), z(t)) of the line that is the intersection of tangent planes at (1,…

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Q: Let S(x) be a natural cubic spline that passes thorugh the points (-1,1), (0,2), and (1,1). Then,…

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Q: Transform the function y=(1)/(2)x right 6 and vertical shrink of (1)/(4)

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Q: Suppose Vf(x, y) = 3y sin(xy)i + 3x sin(xy)], F = ▼ ƒ(x, y), and C is the segment of the parabola y…

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Q: Calculate Vf when f 3x 2- y z' + 4x'y + 2x - 3y - 5 at the point (1, 1, 0).

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