Evaluate the line integral, where C is the given space curve. xyeY dy, C: x = 3t, y = 2t, z 4t, osts1

Q: Q2/ Find T, N, and k for the space curve r(t) = (3 sin t)i +(3cos t)j + 4tk

A: Question: Objective is to calculate the tangent vector T, normal vector N and the curvature κ of…

Q: 2. Sketch the cylinder y = x² +1.

A: complete graph provided below with python code Explanation:  code behind above :  import numpy as…

Q: | Let C be the quarter circle centered at (2,0) that goes from (1,0) to (2, 1). Evaluate the…

A: ∫c y2xdx + 4yxdy=? We know that this form of integral is solved by Green theorem: ∮cP dx+Q…

Q: c) Evaluate the line integral (x+2y)dx -2xdy along the following closed path, the circle x+ y= 25,…

A: In parametric form,

Q: Find . F.dr when F(x,y) = (2x,3y²) and C is only the first quadrant part of a circle of radius 3…

A: Let C be a smooth curve and r→t=xti^+ytj^+ztk^ be the position vector of any point x,y,z on C.…

Q: Evaluate z* + x dS where S is the cylinder x2 + y? = 36 between the planes z = -3 and z = 1,…

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Q: Find an equation of the tangent plane to the surface z = 2y² – 3x² at the point (-3, -3, -9).

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Q: The slope of the surface z = xy² in the x- direction at the point (2, 3) is O 12 O 8 O 1 O 9 O 10

A: The slope of the surface z = f(x,y) in the x-direction at (x0,y0) is given by [∂z/∂x](x0,y0) =…

Q: Use the Jacobian of a coordinate transformation to find the area of the parallelogram bounded by the…

A: We use the following transformation to find the area of the parallelogram bounded by the lines y =…

Q: Find T, N, and K for the space curve r(t) = 8ti + (8a cosh (t/a))j, a>0.

A: Answer

Q: Verify that the half plane above the horizontal line y = k is mapped into the interior of the circle…

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Q: Find a parametric function for the intersection of r – 3y + 4z = 0 and a? + y² = 9.

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Q: Assuming that z is a function of x and y, find the equation of the tangent plane and the equations…

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Q: Find the Surface area of the portión of the cylinder ya + z² =9 above the rectangle in the xy plane.…

A: Cylinder y2 + z2  = 9,z = 9-y2,0 ≤ x ≤ 2,and-3 ≤ y ≤ 3