Let S be the portion of the helicoid parametrized by u cos v u sin v g(u, v) = 0

Q: Consider the helix given by c(t) = (a cos (t), a sin(t), ct). Show that its acceleration vector is…

A: Given helix: We have to show that its acceleration vector is always parallel to the xy-plane.

Q: 3. Consider the following helix with vector equation 7 (t) = 2 cos (t) 7 (t) 7 + tỉ + 2 sin (a)…

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Q: Find ∂w/∂r for w = yz/x, x = θ2, y = r+θ, z= r-

A: To evaluate ∂w∂r

Q: C is an oriented curve segment given by the parametrization r(t) = (cos t, sin t, t), T/4 <t < a/2.…

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Q: 1. Let R and b be positive constants. The vector function r(t) = (R cost, R sint, bt) traces out a…

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Q: Let C be the graph of Ŕ(t) = (t sint, t³). a. Using delta definition, show that Ŕ(t) is continuous…

A: Given that R→t=t sint,t3 To find: (a) R→t is continuous at origin.              (b) unit tangent and…

Q: Let f(x,y)= e, Compute the cartesian equation of the tangent plane r,y) at the point (2.2).

A: The equation of tangent plane

Q: For the curve r(t), write the acceleration in the form a+T+aNN. r(t) = (6t sin t+ 6 cos t)i + (6t…

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Q: Find u · (v ✕ w).

A: Here we have to find the given vector operation

Q: Use a parameterization R(u, v) of f (x,y) = xe*y to find the tangent plane to f(x, y) at the point…

A: Tangent plane at (x1, y1) to f(x, y) is given by below:

Q: Let F(x, y) = -z|. Let C be the curve parametrized by (t, cos(t), sin(t)), where 0 <t<. y Evaluate:…

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Q: The path r(t) = (t- sin t) i+ (1- cos t) j describes motion on the cycloid x=t- sin t, y=1- cos t.…

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