Evaluate the line integral Fdr where F = 4.xyi – 8yj+ 3k and C is a curve given by y = 2x, z = 3 from the points (0.0,3)and (3,6,3).

Q: Evaluate the line integral [[(3.ry² + 6y) dr, where C' is the path traced by first moving from the…

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Q: Find the equation of the tangent plane to the surface y = 2x2 - z at the point %3D (0, -1,-2) y+2z =…

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Q: Determine the equation of the normal line to the surface In (x + y) = Z 2 at the point (-1,2,0)

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Q: Draw the contour curves for h (x, y) _y²+x² -1+2x and c = 0, 2, 4.

A: If the graph of z=f(x,y) is sliced by a plane: z=c, then the two dimensional cross-section obtained…

Q: find the distance from the point P (2,1,1) to the lins x+1 y-1 Z-3 L: 6 -2 -3 = =

A: To find the distance from the point to the line.

Q: Evaluate [(y² - 4xy, 2xy - 2x²). C where C is the line from (0, 0) to (1,5) followed by the line…

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Q: Classify all level curves of f(x, y) = Vy² – x² and draw its contour map.

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Q: Evaluate √(2² + yz sin(xyz))dx+(y²+xz sin(xyz))dy+(x+xysin(xyz))dz where C is the curve following…

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Q: 3. Let f(x, y) = xy+ y². Find the equation of the tangent line in parametric form in the x-direction…

A: Solve the following

Q: Compute F. dr for the oriented curve specified. F(x, y) = (4x2, xy), line segment from (0, 0) to (2,…

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Q: 6. Find an equation of the tangent plane and a set of symmetric equations of the normal line to the…

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Q: Find the tangent plane to the equation z = 6y cos(4x – 2y) at the point (2,4,24) Z =

A: It is given that z=6ycos4x-2y and the point is 2,4,24. Recall the fact that if the equation of the…

Q: Find the equation of the plane tangent to the graph of z + xyz = 33 at (1,2,3).

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Q: Determine the equation of the normal line to the surface z2 cos(x + 2y) at the point (2, –1, 0).

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Q: Find an equation of the tangent plane to the surface at the given point. X²+y²+z²=14, (1,2,3) And…

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Q: Consider the family of curves y I 1+ GI

A: We have y=x1+c1x Differentiate with respect to x: dydx=ddxx1+c1x⇒dydx=1+c1xdxdx-xd1+c1xdx1+c1x2…

Q: 1.. Plot the cardioid curve (0)=2+2 sin then compute all angles for which the slope of the tangent…

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Q: Find the length of the parametric curve x = 2t + 1, y = 3 + 2tž, 0 < t <%.

A: Find the Length of the curve

Q: 2dy -2y 2. zt at

A: Solved below

Q: Find the equation of the tangent plane to the given surface at the point (0,-1,2). y = 2x2 – z2 O y…

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