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

Q: Express the curvature of a twice-differentiable curve r = ƒ(u) in the polar coordinate plane in…

A:

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

A: Given ,

Q: Find the radius of curvature at origin at (0,0) y - x = x2 + 2xy + y2

A:

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

A:

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>0. To Find :…

Q: Calculate the curvature function for r

A:

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

A: Solution

Q: What is the approximate radius of curvature of the function y = x2 + 6x – 96 at the point (8, 16)?

A:

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

A:

Q: What is the equation for curvature for the curvey=sin(x)? What is the curvature of the curve…

A: The equation of the circle of curvature is calculated using the formula: x-x2+y-y2=ρ2, where:…

Q: Find the radii of curvature and torsion at a point of the curve    x^2+y^2=a^2 , x^2-y^2=az

A:

Q: Find the curvature and radius of curvature of the plane curve at the given value of x. y = 9x 4…

A: Given curve is, y=9x-4x Differentiating this with respect to x we get,  dydx=9-4ddx(1x)⇒dydx=9+4x2…

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

A:

Q: Find the radius of the curvature of the curve x =y at (1, 1) +1 Hint: radius of curvature =

A: To find the radius of curvature of curve x= y3 at (1,1)

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: Determine the curvature of the graph of y = In x at the point where x = 1.

A:

Q: Exercise 7. Show that the curvature of a circle of radius r is , and the curvature of the line is…

A: Show that the curvature of a circle of radius r is 1r and the curvature of the line is zero.

Q: |d?y |dx2 K($) = Cos3 %3D

A: Given curve y=f(x)

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

A:

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)…

A:

Q: Show that the curvature of a circle of radius r is K =1/ r.

A: The equation of the circle with radius r is y=±r2-x2. The upper portion of half circle equation is…

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

A:

Q: Find the curvature and radius of curvature of the plane curve y = tan x at the given value of x == π…

A: To find the curvature and radius of curvature of the plane curve y=tanx at x=π4.

Q: At what point does the curve have maximum curvature? y = 4ex (х, у) %3D What happens to the…

A:

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

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Q: Find the curvature of a superellipse defined by the parametric equations…

A:

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

A:

Q: Find the curvature of y = sin(-lx) at x = .

A: Solution:-

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

A:

Q: Find rectifying plane of et, é, t at the curve t%3DL

A: Given curve is αt=et,e-t,2t.  To find the rectifying plane of the curve . Result: Let rt→=xt,yt,zt…

Q: Find the curvature and radius of curvature of the plane curve at the given value of x. y = x3, x = 2

A: Consider the following equation of curve: y=x3 Differentiate y with respect to x: dydx=ddxx3y'=3x2…

Q: he normal vector to the tangent plane for the surface point (1, 2, -1) is: Select one: None of them…

A: topic:- application of derivatives

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: Find the point on the curve y = ex where the curvature is greatest.

A: Given: Find the point on the curve y = ex where the curvature is greatest.

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

A:

Q: Find the curvature of the plane curve y = 4t³ at the point t = 2.

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Q: Calculate the curvature and radius of curvature of y = 4 cos x + sin x at x = π/2

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

A:

Q: Determine the radius of the curvature of the plane curve given by y In sec x at the || point (0,0).

A:

Q: Determine the curvature of the curve y=arctanx at x=0 and at infinity.

A:

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

A:

Q: Find the curvature and radius of curvature of the curve y=cosmx at a maximum point.

A: Given curvey= cos mxWe have to find curvature and radius of curvature at maximum point .Formula…

Q: The curvature of y = x2

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