Suppose r(t) = i+t²j+2tk. Find the length of the portion of this curve that goes from the point G, 1,2) to (9,9,6). Also, give an expression for the curvature as a function of t.

Q: Find the curvature k of the curve C : 16 =1 at the point (0, 3)

A: 1. convert the equation into parametric form 2. use formula for curvature written below

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

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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 an equation for the tangent plane to the surface 22 – xy? = 0 at the point (1, 3, 3).

A: Given that At point (1,3,3) Take, Now to find the divergence of f, The divergence at point…

Q: Find the curvature k of the curve r = (t,t², 5)

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

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: 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 of the curve r(t) =

A: This question can be solved by applying the formula for curvature.

Q: Find the curvature K of the curve at the point P. r(t) = 4ti + 3tj, P(-4, 3)

A: Given,          rt=4t i+3t2 j , P-4,3We know that,           The curvature K of the curve is given…

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

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Q: Find the curvature k of the circle C : (x – 2)² + (y + 3)² - at the point (5, 1).

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Q: Find the curvature K of the curve. r(t) = 5ti + 2tj %3D

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Q: Find the curvature k of the curve C : 16 = 1 at the point (4, 0)

A: Curvature K of curve is : -16/3

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

A: WE HAVEDB/DS = τNWHERE AT ANY POINT P[X,Y,Z] ON THE CURVEB IS UNIT VECTOR CALLED BINORMAL TO THE…

Q: Let R be a vector function whose graph is smooth curve such that, R(2) =, R'(2) = , and R"(2) =…

A: Radius of curvature of teh function is given by formula, R = (1+y'(x)2)32y''(x)

Q: Find the curvature K of the curve at the point P. r(t) = ti + t2j + k, Р(2, 4, 2)

A: Given

Q: Find the curvature K of the curve at the point . r(t) = 2ti + 4tj, P(-2, 4) K =

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Q: Find the equation of the tangent plane to the surface z = 4 号+ゾ + y² at the point (2, -3, 10)

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Q: Suppose I → R³ is a regular curve -c3 with zero curvature anywhere zero, and then the H-curve holds…

A: A given regular curve with zero curvature is -c3 We change in terms of t, then the regular curve is…

Q: Find the curvature K of r(t)= 2ti +t²j - k 3

A: We know that, the expression for the curvature; kt=r→'t×r→''tr→'t3 Given r→t=2ti→+t2j→-13t3k→

Q: Use Theorem 11.24 to prove that the curvature of a linearfunction y = mx + b is zero for every value…

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Q: Find the curvature k of the curve C: 16 =1 at the point (4, 0)

A: Given The curve C : x216+y29 = 1  We have to find the curvature κ of the curve at the point 4, 0.

Q: Find the curvature for the following vector function. 1. r(t)=( 4t, -t², 2t³)

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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 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 & y=2t2 Now put x=-3 & y=2, we get -3=3t…

Q: Find the curvature k of the circle C:(x – 2)2 + (y +3) = 25 - at the point (5, 1).

A: circle equation is x-22+y+32=25 and point 5,1find curvature k

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

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

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Q: Find the curvature K of the curve C x² 1 16 9. at the point (0, 3)

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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: Find the curvature of the curve given by r(t)=(4sint, 4, 4cost)

A: Given that : r(t)=4sint, 4, 4cost Therefore, r'(t)⇀=4cost, 0, -4sint. Therefore,…

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) =<2t, - 3sin t, 3cost)

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Q: Given the curve f (t)= (2t2 - 3, 3 - t, 3 + 2t?). Find the equation of the line parallel to the…

A: Consider the equation as shown below: Here, curve ft =2t2-3, 3-t, 3+2t2 Here, the object is to find…

Q: Find the curvature k of the curve r(t)=ti+ 6t^2j+4tk

A: To find: The curvature k of the curve rt=ti+6t2j+4tk. Formula used: The curvature of curve is…

Q: For each KeR+, HeR make a curve-C3 y:R –→ R³such that it has a constant curvature K and a constant…

A: We produce a curve γ:ℝ→ℝ3 , so we have γt=cost, sint,t.  Now finding its first and double…

Q: Find the curvature k of the curve C: 16 + =1 at the point (0, 3)

A: To find the curvature of the curve at the point (0,3).

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: Show that for a plane curve the torsion T = 0.

A: We have to shown that, For a plane curve the torsion T=0

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

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Q: (b) Find the curvature for the space curve r(t) =(1.",)at the point.1.11 using the formula 10.

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Q: Find the curvature K(t) of the curve

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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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