If 7 (t) =< 2cost, v3 t, 2 sint > then the curvature at the point (2,0,0) is (A) (B) 25 (c); (D)를 (E) -

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: 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: Consider points P and Q on a curve. What does it mean for the curvature at P to be less than the…

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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: Find the ordinate of the center of curvature of the curve y² = 4x at point (2, 4) from the x-axis.

A: Given option are wrong, option c should be '-16'.

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: Show that the parabola y = ax2, a ≠ 0, has its largest curvature at its vertex and has no minimum…

A: Using the relation,

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

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Q: Prove that the parabola y = x^2 at the points where the line has an angle of inclination "o" the…

A: Curvature of  a graph y= f(x)  k=d2ydx21+dydx232

Q: 2.Let a be a unit speed curve lying on a sphere center c and radius a > 0. Find the minimum value of…

A: Given That : Let α be the unit speed  curve lying on a sphere center c and radius a&gt;0. To Find :…

Q: -*) at (0, 1). Find the center of curvature of the curve

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Q: 4. Does there exist a simple closed unit-speed plane curve with curvature less than or equal to 2…

A: In a simple closed unit-speed plane curve, curvature =1r According to the question, Area of the…

Q: Q2 Find the radius of curvature of yv5 = x' at the point (x, y,). Hence, show that the radius of…

A: Use formula of radius of curvature

Q: Find the curvature and the radius of curvature of the curve y = x + 5x2 – 2x3 at the origin (0,0).

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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: Show that curvature at an inflection point of a plane curve y = f (x) is zero.

A: We have to show that curvature at an inflection point of a plane curve y=fx is zero. We know that if…

Q: b.) show that brnormal of the muolute the unit *-ズ+(c-s)で g =dG) |k-s) K| K* where K is the…

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Q: Find the radius of curvature of 6y = x³ at the point (2,).

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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 curvature of the curve defined by the function y=3x^2 - 2x + 4 at the point x=2

A: Curvature is defined as : K(x) = |y"(x)| / {1 + [y'(x)]^2}^(3/2).  Note that :- |y"(x)| means the…

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: What is the radius of curvature at point (1, 2) of the curve 4x – y2 = 0.

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

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Q: 4) Find the families of lines of curvature of the surface : =+ y² .

A: Given: z=x2+y2

Q: The curvature of y =x is

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 of r(t) = at the point (1,0,0)

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

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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: Show that the parabola y = ax2, a  0, has its largest curvature at its vertex and has no minimum…

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

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Q: Find the curvature of the parabola f(x)= ax +bx+c at its vertex 2a ’

A: Hello. Since you have posted multiple questions and not specified which question needs to be solved,…

Q: Find the y coordinate of the center of curvature of the parabola at (2,2). 7. -7 -6 6.

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Q: Exercise 2. Show that the total geodesic curvature of a simple closed planar curve is 27.

A: We will use the Tangent-Normal frame to prove the given result.

Q: Let 3 : (3t, r = be a curve in 3-dimensional space having unit tangent and normal vectors u and .…

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

A: Consider the given equation as x=acost, y=bsint and a&gt;b&gt;0

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

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Q: What is the radius of curvature at point (1, 2) of the curve 4x - y2 = 0.

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

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Q: Find the curvature of rt) = Point (2,0, "2) P"(t)=(2Binf-9 Coo(3t), 0> k(4.0%)

A: Given rt=2sint, cos3t,t at point 2,0,π2r't=2cost, -3sin3t,1r''t=-2sint, -9sin3t,0

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)