Find the curvature. r(t) = 5t i + 5t j + (5 + t?) k x(t)

Q: Find the curvature K of the curve. r(t) = 4 cos 2rti + 4 sin 2rtj K =

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Q: 04. Show that the Gauas and mean curvatures on, X-(u+v,u-v, uv) at u=1, v=1 are K=1/16 and H= JI.…

A: Given: 1) X=(u+v,u-v,uv) at u=1,v=1. 2) The paraboloid is xy=aZ.

Q: Q2/Find the curvature of the curve, r= (4 cos n i+4 sin n j)

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Q: Find the curvature and radius of curvature of the plane curve at the given value of x.

A: Given that: The equation is y = e-x4 and the point x = 8 .

Q: 2. Show that if a : [a, b] → R" is a regular parameterization of a curve then the curvature at α(t)…

A: Let, is a regular parameterization of a curve. To show the curvature at  is .

Q: Find the curvature of the curve r(t) = e2ti + e2t cos tj + e2t sin tk.

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Q: Find the curvature and the radius of curvature at the point t = 0. x = e' cos(t), y = e' sin(t), z =…

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Q: Find the curvature and radius of curvature of the parabola y=x² at the origin. O K= 2, p=1/2 O k=2x,…

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Q: Find the curvature and the radius of curvature at the point t = 0. x = e cos(t), y=e¹ sin(t), z =…

A: Let's find.

Q: Find the curvature of the curve r(t) = 4ti + 3 cos tj + 3 sin tk .

A: curve r(t) = 4ti + 3 cos tj + 3 sin tk . We need to find the curvature of the given curve.

Q: Find the curvature and the radius of curvature at the point t = 0. %3D = e' cos(t), y = e' sin(t), z…

A: Given

Q: Find the curvature and the radius of curvature at the point t = 0. x = e cos(t), y = e sin(t), z =…

A: Basic calculation of vector is required

Q: Find the curvature and radius of curvature of the plane curve at the given value of x. y = x - 32 ,…

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Q: Find the curvature and the radius of curvature at the stated point for r(t) = 3cos t ax + 4sint ay…

A: Given function is rt=3cost ax+4sint ay+ t az To find curvature and radius of curvature

Q: Find the curvature K of the curve at the point P. r(t) = Pi + tj + 1, 3 2 K = %3D

A: Given that rt=12t2i+tj+13t3k and point is P12,1,13. It is required to find the curvature K at the…

Q: Q2/Find the curvature of the curve, r= (4 cos n i+4 sin n j) .n=(In 2t)

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Q: Find the curvature and the radius of curvature at the stated point. r(t) = 10 cos(t)i+11…

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Q: The curvature of y=x? is: None .a 1 (1+4x)/2 .b O (1-4x2)2 .cO -1 (1+4x)2 .d o «17 jo 4 Jiull uo…

A: In this question we have to find the curvature of the given function which we can find out by using…

Q: Find the curvature and the radius of curvature at the stated point for r(t) = 3cos t ax + 4sint ay +…

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Q: Use this theorem to find the curvature. r(t) = 2ti + 5 sin(t)j + 5 cos(t) k K(t)

A: →dcos(t)dt = -sin(t)→dsin(t)dt = cos(t)→ If, r→=a i + b j + c k    Then,  r→ = a2 + b2 + c2

Q: A particle is moving in space with position function R(t) = (cos(4t), sin(4t),5 – 3t) Find the…

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Q: Find the curvature of r(t) = (2 cos(t), sin(t), 3) at t = = 1.

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Q: Find the curvature of the curve r(t). r(t) = (3 + 6 cos 9t) i - (8 + 6 sin 9t)j + 6k %3D

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Q: Find the radius of curvature of the curve r=t°i+ 2t´j- - tk at the point where t= 1

A: Since you posted multiple question in this question which are not interlinked so i have solved first…

Q: Find the curvature K of the plane curve at the given value of the r(t) = 4ti – 4tj, t = 1 K =

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Q: Find the curvature of the given curve r(t) = 5ti +3sin(t)j + 3cos(t)k a. 2//34 b. 4//34 C. 3/34 d.…

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Q: Find the curvature and radius of curvature of the plane curve at the given value of x. y =e-x/4, x =…

A: The given curve y=e-x4  ,  x=8

Q: Q2/Find the curvature of the curve, r= (4 cos ni+4 sin n j) .n=(In 2t)

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Q: Find the curvature K of the curve. r(t) = et cos(t)i + et sin(t)j + et k

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Q: Find the curvature and the radius of curvature at the stated point for r(t) 3cos t ax + 4sint ay + t…

A: r(t)=3cost, 4sin t,t, t=π2 find r'(t) and r''(t) r'(t)=-3sin t,4cos t,1r''(t)=-3cos t,-4sin t,0 To…

Q: Find the curvature K(t). r(t) = (4t, 3t, 2) %3D

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Q: Find the curvature k(t) of the curve r(t) = (-1sint) i+(-1sint)j+(-4 cos t) k %3D

A: Given : rt=-sinti+-sintj+-4costk To find : curvature κt Curvature is given by  κt=r't×r"tr't3…

Q: Find the curvature of the curve r(t) = 2ti + 5 cos tj + 5 sin tk

A: The given curve is rt=2ti+5cost j +5 sint k. This implies that, r't=2 i-5sint j +5 cost kr''t=0…

Q: Q11

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Q: Find the curvature of the space curve. r(t) = - 3i + (3+2t)j + (t +8)k %3D

A: The given curve    r(t)=-3i+3+2tj+t2+8k

Q: Find the curvature and the radius of curvature at the point t = 0. x = e' cos(t), y = e' sin(t), z =…

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Q: Use this theorem to find the curvature. r(t) = 9t i + 2 sin(t) j + 2 cos(t) k

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Q: Find the curvature of r(t) = (t, 5, t²): at a general point, and at (1,5,1).

A: Given r→t=t,5,t2 and point is 1,5,1. We have to find the curvature of r→t=t,5,t2 at point 1,5,1 The…

Q: Find the curvature and the radius of curvature at the stated point for r(t) = 3cos t ax + 4sint ay…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: 10.) At what point does the curve have maximum Curvature? y=In(x). K(x)= f"|

A: firstly find f, f' and f'' . And substitute all these values in given curvature formula.  After that…

Q: Suppose r(t) = i+t²j+2tk. Find the length of the portion of this curve that goes from the point G,…

A: We will find out the required value of length and expression for curvature.

Q: If 7(t) = then the curvature at the point (2,0,0) is

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Q: Find the curvature of r(t) at the point (1, 1, 1). r(t) = (t, t², t³) k=

A: Given: vector valued function r(t)=<t, t2, t3>To Find: curvature at t=1

Q: Find the curvature and the radius of curvature at the point t = 0. x = et cos(t), y = et sin(t), z =…

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Q: At what point does the curve have maximum curvature? y = 7 In(x) (x, y) = What happens to the…

A: Given,              y = 7 ln(x)

Q: Find the curvature κ(t) of the curve r(t)=(−4sin(t))i+(−4sin(t))j+(−5cos(t))k

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Q: Find the curvature and the radius of curvature at the stated point for r(t) = 3cos t ax + 4sint ay +…

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