|axv Use the alternative curvature formula x =- to find the curvature of the following parameterized curve. r(t) = (4 + 51? ,21,0)

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 a formula for the curvature of the function P= nrt/v-nb - (an^2)/(v^2) ,where n, R, a, b,and T…

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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: If7(t) = then the curvature at the point (2,0,0) is %3D (A) (B) (C) (D) (E)

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Q: Determine the maximum curvature for the graph of f(x) = 6 In (3x). The maximum curvature is at x =

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Q: Chapter 12, Section 12.5, Question 013 Find the curvature and the radius of curvature at the stated…

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Q: Chapter 12, Section 12.5, Question 013 Find the curvature and the radius of curvature at the stated…

A: The given vector-valued function is rt=6cost i+6sint j+7t k at t=π2 to find the curvature and the…

Q: a aa Jll J l a Find the curvature of 7 (t) - ( cos (2t)- sin (2t),4t>. a Jall JA psl ING A FUJITSU

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Q: a) Find a plane curve whose signed curvature is given by k,(s) where a is a positive constant and s>…

A: The given signed curvature is ks(s)=12as

Q: For the function graphed below, estimate the point of greatest curvature. 43 Submit Question

A: We have to find greatest curvature of the function in graph

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: Question S. Find the radius of curvature of the curve rít) = (2 in)i- at point (0,-2).

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

A: The complete solutions are given below

Q: Show that any straight line has curvature zero. Conversely, if a smooth curve has curvature zero,…

A: Note:- Curvature k=d2ydx21+dydx232   Given that a straight line and show that it has curvature zero.…

Q: The curvature of r = 1+ cos 0, 0: 2 2/2 5 2/2 3/3 2 3/3 3.

A: Given: r=1+cosθ,θ=π2 κθ=2f'θ2+fθ2-fθf"θf'θ2+fθ232   r=f(θ)r=1+cosθ f'θ=-sinθf"θ=-cosθ

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: For a function y = f(x), show that the curvature is given by к(x) = Hint: Parameterize the function…

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Q: The curve in the figure below is parametrized by F(t) = (t³ – 3t) · i + (3t² – 2) · j, for -00 <…

A: Here, the given parametric curve is: r→(t)=(t3-3t) i +(3t2-2) j

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: (b) Find principle curvature of X(u, v) = (u cos v, u sin v, bv).

A: Given that X(u,v)=(ucosv,usinv,bv) Take the derivative with respect to u, dXdu=(cosv,sinv,0) Take…

Q: Find the curvature K of the curve at the point P. r(t) = 1/2t2i + tj + 1/3t3k,    P (1/2, 1, 1/3)

A: The curvature is given by kt=r't×r''tr't3. Given that rt=12t2i+t j+13t3k. Obtain r't as follows.…

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

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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 K of the curve. r(t) = etcos(t) i + etsin(t) j + et k

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Q: 11) Example: of R' (t) to find the curvature Use the Theorem in 10 to

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Q: Find the curvature of r(t) = at the point (1,0,0)

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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: laxv to find the curvature of the following parameterized curve. Use the alternative curvature…

A: Given: And Here, v = r'(t) and a = r''(t). So,  by using the above formula and r(t) we will now…

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

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Q: The curvature of y=x is: None .a O 1 (1+x?)/2 .b O (1-x*)/2 .c O -1 (1+x²)/2 .d o

A: We will use the fact that the curvature of y=f(x) is given by…

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

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

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Q: Find the curvature K and the radius of curvature R at (1,2). (A K= √/2. R=₁ R = √2 (В) K= R= 2√2 2√2…

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Q: 6. Determine the curvature of (a) t) = (3cos t, 4 sin t, t) (b) Ft) = (e' cost, e' sint, e)

A: a) Given:         r→(t)=3cost,4sint,t   The formula for curvature k(t)=r→'(t)×r→''(t)r→'(t)3…

Q: For a function y = f(x), show that the curvature is given by к(x) = Hint: Parameterize the function…

A: Show that the curvature is given by kx=f''x1+f'x232

Q: YouTrylt 3 Compute the curvature of a curve. r(t) = (acost, asin:) for a 20, (a) Compute the…

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Q: For the function graphed below, estimate the point of greatest curvature -4 -3 /-2 -1 -2 (0,-2) x…

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

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Q: Determine the maximum curvature for the graph of f(x) = 7 In (2x). The maximum curvature is at x=

A: We are given function f(x)=7ln(2x) of the graph Formula for curvature is κ(x)=|f′′(x)(1+(f′(x))2)32|…

Q: Find the curvature of r(t) = (2t, t²,-t³) as a function of the parameter t. Simplify your answer to…

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Q: Consider the curve y(2) = sin z. Which one of the following statements is true? O The curvature at =…

A: Here to find curvature of curve, y(x)=sin(x) Curvature of curve is given as,…

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

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Q: Find the radius of curvature of the curve x^2 y=a(x^2+y^2) at the point (–2a,2a).

A: Consider the given function. x2y=ax2+y2y=a1+x-2y2 Now, find the derivative of y with respect to y.…

Q: The curvature of y = x2

A: so we have to find curvature of y =  x2. we use the formulae for curvature  k(x) =…