The Cornu spiral is the plane curve r(t) = ⟨x(t), y(t)⟩, where x(t) = Z t 0 sin(u2/2) du, y(t) = Z t 0 cos(u2/2) du

Q: Find a function y = f(x) that describes the parametric x = -2t + 1, y = 3t², for – o <t < ∞. curve

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Q: Find the arc length of the space curve given by the vector equation r(1) = (- 9t + 16) + (-9² +…

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Q: Given w f(z,y, 2) = zy²z. Find: Ograd/(1,3,-2) 3. (b) equation of the tangent plane to the surface…

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Q: Find three different parametrizations of the graph of y = x3.

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Q: For which values of t is the parametric curve x=8t, y=t+t, -0c0s ts 00 concave up? (Enter your…

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Q: Let y : IR → R be the parametric curve Y(t) = (, t, t). Find the coordinates of a point P on this…

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Q: П π Find T, N, and k for the plane curve r(t) = 7t i +7 In (cost) j. - <t<2.

A: Since you have uploaded multiple questions according to our guidelines we have solved first question…

Q: π The path r(t) = (6 cos t) i + (6 sin t) j describes motion on the circle x² + y² = 36. Find the…

A: Given, r(t)=(6cos t) i+(6sin t) j Path of the motion described by x2+y2=36 To find : velocity and…

Q: 3xyz = 63 and 3x² + 4y² + 8z² = 423 at point (−3, 1, −7). ř(t) = with -∞ < t <∞

A: The parametric form of a line that passes through x0, y0, z0 and has the direction ratios: a, b, c…

Q: Sketch the curve with the given vector equation by finding the following points. r(t) = (2, t, 4-t²)…

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Q: sider the curve C defined by the equations x = t° + 3t? and y = 2t + 15t2 + 36t + 6. Show that C is…

A: We have to show that Given curve is smooth.

Q: Let F(x, y, z) = (6xyz+4x) i+(3x²z+ze")j+(3x²y-e=v) k, and let C be the portion of the parametric…

A: Given F→x,y,z=6xyz+4xi^+3x2z+ze-yj^+3x2y-e-yk^ And C be the portion of the parametric curve given by…