Calculate the mean curvature of the catenoid 2²+ y? 2= a1 a

Q: Calculate a curvature of the curve r(t) → = ⟨t,t2,t3⟩ at point (4,16,64)

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Q: Find the curvature of r(t) = (In t, 2t, t²) at (0, 2, 1).

A: Given r(t) = <ln t, 2t, t2> To find the curvature (k) at (0, 2,1)

Q: Find the curvature of the plane curve at the pointindicated. y = e^t , t = 3

A: y=et,  t=3 Differentiating with respect to t, we get dydt=et Again differentiating with respect to…

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 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: 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: Find the curvature and radius of curvature of the parabola y=x2 at the origin.

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

A: Solution

Q: Find the curvature of the curve given by r(t) = 2ti + t2j −( 1/ 3) t3k.

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

A: Curvature Formula: k=y''1+y'232

Q: Calculate the curvature function κ(t). r(t) =〈4t + 1, 4t − 3, 2t〉

A: Given: r(t)=4t+1,4t-3,2t Differentiate the function. r'(t)=ddt4t+1,4t-3,2t=4,4,2 Again…

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: At what point does the curve have maximum curvature? y = 9 In(x) (x, y) = (| 6.3639, – 6.3639 What…

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Q: Show that along the plane curve x = #1(t)e, +2(t)e2 the curvature is 4.30. [(a)2(5)213/2 a0 + 3

A: The curvature K at a point of a curve defines the speed of rotation of the tangent of the curve at…

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: Find the center of curvature of the curve y at (0, 1). (A) (0, 2) B) (1, 1) c) (0, 3) D) (0,0)

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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: Given y =e^(-x/4)  ,x=8 Now we have to find curvature and radius of curvature at x=8

Q: Write a formula for the curvature of a plane curve with equation y = f(x). %3D

A: If the equation y=fx. Then the formula of radius curvature at the point is:   Rx=1+dydx232d2ydx2…

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: 3. Find the radius and center of curvature of the parabola y=x²-4x+4 at any point (x,y)on the curve.

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Q: Find the currvature and radius of curvature of the plane curve at the given value of x. y%3D 5x+ 7.…

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

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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: Find the curvature of r(t) = √√7ti + etj + e-k at point P(0, 1, 1).

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Q: Write a formula for the curvature of a plane curve with equation y= f(x)

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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 radii of curvature and torsion at a point of the curve r? + y2 = a², x² – y? = az. %3D %3D

A: Given curve is x2+y2=a2x2-y2=az

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 the cardioid r=a(1+cosθ) at θ=0.

A: Given equation of cardioid is Derivatives of polar curve are

Q: Find the curvature of the curve. r(t) =<2t, - 3sin t, 3cost)

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Q: Q11

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

Q: Find the following for the hyperboloid of one sheet (a) First and second fundamental forms (b)…

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Q: Show that the Gauas and mean curvatures on , X = (u + v,u –- v,uv) at u = 1, v = 1 are K = 116 and H…

A: Given, X=u+v,u-v,uv u=1,v=1 , k=116 and H=182 We know that, E=xu,xuF=xu,xvG=xv,xv So, we need to…

Q: 4. Find the curvature of r(t) = (tv2, e', e-t) at the point (0,1,1).

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Q: Find the gaussian and mean curvature functions of the surface m given by the equation y3=y1y2 in R³…

A: First parameterized the equation.

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: Example: Find the curvature of the curve, where a&b> o r= (acos ti + asintj+ btk)

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Q: What is the radius of curvature of the polar curve r = 02 at 0=3/2?

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Q: 1) Calculate the curvature of the position vector 7(t) = sin tax + %3D 2cos tay + V3 sin tāz is a…

A: In this question we have to find curvature and radius of curvature.

Q: Consider the plane curve parametrized by F(1) -i+ (In(com(1)J, Find curvature s(4).

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

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