Find the length parameter of the curve r(t) = < 7cos t, 7sin t, 10t > with base point at ( 7, 0, 0 ).

Q: Q1) Find equations of the Normal plane and Osculating plane of the curve y = 2t, x = 2 sin 3t , z =…

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Q: The parametric curve x= 414 + 412 + 1, y= 5t 3 – 5t has two tangent lines at the point (9, 0). Find…

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Q: II. r*yz dxdydz K = {(x. v. z) : 0<x<1, 0 <y<r. 0<z<z°u}

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

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Q: x = 2 + 3t, y = cosh 3t , 0 <y<1

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A: Given α(t)=(t,t22,t36)

Q: Find the length of the curve. The curve r= 8,/1+ sin(20), 0 <0< 4 A) 27 C) 8(7+ In(m

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Q: Q4) Show that the point (-1, 0) lies on the curve 6x² + 3xy + 2y2 + 17y – 6 = 0. Then find the…

A: Put x=-1 and y=0 in the equation of curve that is…

Q: Find the slope of the parametric curve x = -2t3 + 1, y = 3t2, for - ∞ &lt; t &lt; ∞, at the point…

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Q: Find the angle between the curve 2y=e-x/2 and y-axis

A: we will see in next step

Q: Find the length of arc from (2,1) to (4,4) of the curve x = 2√y

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Q: A cycloid has parametric equations z =t - sint, y = 1 - cost, 0 <t< 2x. Find the slope of the…

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Q: Let Q = 4x2 + 6xy+ 4y? . The points on the curve Q = 7 which are closest to the origin are: %3D %3D…

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Q: Q4) Show that the point (-1, 0) lies on the curve 6x2 + 3xy + 2y2 + 17y - 6 = 0. Then find the…

A: Substitute x=-1 and y=0 in the given equation Then 6(-1)2+3(-1)(0)+2(0)2+17(0)-6=0

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 C be the curve connecting (0,0) to (9,3) to (-3,3) to (0,0) using straight lines. Evaluate (sec…

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Q: T Find T, N, and k for the plane curve r(t) = -7 In(sect)i-7tj, -<t<2 T(t) = (i+) (Type exact…

A: Given r(t)=-7 ln(sec t) i-7t j Differentiate r(t) w.r.to t; r1(t)=-7. 1sec t[sec t.tan t] i - 7…

Q: find the frenet apparatus of curve 3u-u3  , 3u2 , 3u+u3 and  Find equations of tangent, normal and…

A: Given that 3u-u3,3u2,3u+u3 The fernet apparatus of the curve is, dTdu=kNdNdu=τB-kTdBdu=-τN Where T,…