If 7(t) =< 2cost, V3 t, 2 sint > then the curvature at the point (2,0,0) is

Q: Find the curvature of the parabola given byy = x −(1/ 4)x2at x = 2. Sketch the circle of curvature…

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Q: Find the curvature of y = sin(3T) at a = =.

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

Q: Let r= (3v/2t, 3ť, /2t³) be a curve in 3-dimensional space having unit tangent and normal vectors u…

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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: find the radius of curvature at any point on parabola y2=4ax

A: Given:  y2 = 4axTo find: The radius of curvature at any point on the given parabola. Formula used:…

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

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Q: Find the radius of curvature of a parabola y² - 4x = 0 at the point (4,4). 2

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Q: Find the radius of curvature at any point on parabola y2=4ax

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Q: 4. At the point (0, 0) the graph of y 4.x2 has greater curvature than does y 2x2.

A: These equation represents parabola,then Radius of curvature: K=  y'' /([1+(y')²]^3/2)

Q: Find the radius of curvature of the parabola y² = 4px at (0, 0).

A: Given that the parabola y² = 4px  To Find the radius of curvature of the given parabola at (0,0).…

Q: What is the curvature of the path of the motion at t=1

A: Since velocity is given we need to calculate  r''(t) only at t=1

Q: Find the curvature of the curve y = x^3 at the point (x, y) = (2, 8).

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Q: 3. Find the curvature of the curve given by 7(t) = (t, t², t) nt (-1, 1, –1).

A: Given curve is We know that curvature to given curve at point (-1,1,-1) , that is at t=-1 is

Q: Find the curvature of y = sin(3x) at a = 프 4

A: We Know that The curvature measures how fast a curve is changing direction at a given point.

Q: Find the extreme values of the function z= &r+2ry-3r+y+1 and show that only one of the two extrema…

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

Q: 3. (a) Find the curvature (t) for the vector-valued function (t², 2t, In t), t > 0. (b) Find where…

A: Basic identities of differentiation and vector calculation are used

Q: Find the center of curvature of xy = 4 at (2, 2).

A: Solution

Q: 4) Find the curvature of y = cos x at the point (÷,²). Then find the equation of the osculating…

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Q: Find the center of curvature of the curve y =-(e*+e) at (0, 1). (А) (0, 2) в) (1, 1) с) (0, 3) D (0,…

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Q: The radius of curvature of the curve r = 4cos 20 at 0 = is %3D 4

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Q: Q2 Find the radius of curvature of y5 =x at the point (x,v.). Hence, show that the radius of %3D…

A: The curve is y5=x3

Q: 2-Show that the regular curve a = a(s) is a straight line if and only if its curvature k is…

A: Here we have to show that a regular curve is a straight line if and only if, its curvature is…

Q: 4. Find the radius and center of curvature of the curve y=6x-x³ at the point (1,5).

A: This question is based on radius and centre of curvature formula.

Q: Find the center of curvature of y = x3 at the point (1, 1) A. (-4, 8/3) C. (6, -2/3) B. (4, -8/3)…

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Q: True or false: the curvature of,k, for x^2+y^2=100 is larger than for x^2+y^2=1/4

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Q: Find the curvature of the curve r(t) = (3 + t, – 4+ 2t, – 2 – t) at the point t = - 8.

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Q: Find the curvature of the curve r (t) = (- 5+ 4t, 1+ 3t, 5t) at the point t - 7.

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Q: Find the curvature of the curve r(t) = 3ti + 2t2j at the point P(−3, 2) .

A: rt=3ti+2t2j Comparing with rt=xi+yj, we get x=3t &amp; y=2t2 Now put x=-3 &amp; y=2, we get -3=3t…

Q: At what point does the curve y = e have maximum curvature? What happens to the curvature as x → ∞?

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Q: 1. Find the points on the parabola y 8x at which the radius of 125 curvature is 16

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Q: Find the curvature k of the curve given by r(t) = (2t²,t, ¿ť²)

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Q: Find the y coordinate of the center of curvature of th parabola at (2,2).

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Q: Find the center of curvature of the curve y=Inx at (1, 0). A) (4, 3) (в) (3,4) c) (3, -2) D (-2, 3)

A: Ans D

Q: 15. y= 2x +3 at x = 27

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Q: Find the curvature of the plane curve y=2t^4 at the point t=2 κ(2)=

A: The given curve y=2t4

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: The curvature of y=x? is:

A: The curvature of a curve is defined as the amount by which a curve deviates from being a straight…

Q: find the curvature of y=x^4 at (1,1).

A:

Q: Find the curvature of the plane curve y = -t at the point t = 2. к(2) -

A: Given:y = -t4differentiating with respect to t, we get:            y' =     d(-t4)dt…

Q: The particle travels along the path defined by the parabola y = 0.5x^2. What is the radius of…

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Q: 8. Find the curvature of the vector-valued function r(t) = at the point t = -1.

A: given function is rt=3t2,-4t,1t find the curvature at t=-1 k=r→'t×r→''tr→'t3

Q: A parabola has an equation of y²=2x, compute the radius of curvature at point (2, 2)

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Q: Show that if M" has constant sectional curvature C then Ricci and scalar curvature of M" are Ric =…

A: We know that from given data: If M has a constant sectional curvature C , k. The Uniqueness of this…

Q: .3 Find the radius of curvature of y=x' at x=1,

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Q: Find the curvature K of the plane curve y 3 at x = 3. 2х + K =

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Q: 8) If curvature of a space curve at (2,3) is 8 and curvature at (7,1) t=7 is 1, what can be said…

A: Given that curvature of a space curve at 2,3 is 8 and curvature at 7,1 is 1.

Q: Show that the ellipse x = a cos t, y = b sin t, a&gt; b&gt;0, has its largest curvature on its major…

A: The curvature for a parametrized curve c(t) = x(t)i + y(t)j is :

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)