p(u, v) = (v, vcosu, vsinu) of surface , Find the Gaussian and its mean curvature at the point P(1,1,0)

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 the curvature and radius of curvature of the plane curve at the given value of x . y = x −4/ x,…

A:

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: 3) Find the radius of curvature for the parametric curve e-t cost , y = e-t sin t.

A: Given parametric curve is x=e-tcost, y=e-tsint. We know that the Radius of curvature of a parametric…

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 curvature and radius of curvature of the plane curve at the given value of x.

A: We have,   It is known that radius of curvature is given as, Here K is curvature of the curve.…

Q: A point moves along the intersection of the elliptic paraboloid z = 10x + 11y and the plane y = 1.…

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

A: Solution

Q: Find a unit vector normal to the surface x^3- xyz + z^3 = 1 , at the point (1, 1, 1)

A: To find the unit normal vector to the surface x3-xyz+z3=1 at the point 1, 1, 1

Q: Find a vector which is tangent to the curve of intersection of the surfaces z = x² – y? and xyz + 30…

A: We will find out the required tangent vector.

Q: 3) Find the radius of curvature for the parametric curve e-t cost, y = e-t sin t.

A:

Q: A point moves along the intersection of the elliptic paraboloid z = a2 + 3y? and the plane y = 1. At…

A:

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 vector (x, 2y, –3z) is normal to the surface x2 + 2y? – 32 – 4 = 0 at any point (x, y, z). - - -

A: Let's find.

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

A:

Q: Consider the sphere x² + y² + z² = 9. Please find the equation of the plane tangent to this sphere…

A:

Q: at a unit-speed regular parametrised curve 3: (-7, 7)→ R² with T, N) has constant curvature k> 0.…

A: Sol

Q: Find the normal vector to the surface z = xe™Y at the point (2,0, 2).

A:

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: |x'y" -y': y'a - y'= es K(t) = (x2 + у'?

A:

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

A:

Q: A point moves along the intersection of the elliptic paraboloid z = 3x² + 5y² and the plane y = 4.…

A: We are given the curve Z=3x2+5y2 and y=4   Now we know that the rate of change is simply derivative…

Q: Compute the mean curvature of the surface z = xy at the origin

A:

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

A: Consider the provided equation, y=sin2x,   x=π4 Find the curvature and radius of curvature of the…

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…

A:

Q: find the points on the surface + z² = 1 that have their tangent plane perpendicular to the vector…

A: For tangent plane of the surface f(x,y,z)=k at a given point normal vector to tangent plane  will be…

Q: Find the curvature function κ(x) for y = sin x. Use a computer algebra system to plot κ(x) for 0 ≤ x…

A: Extreme Points of sinx:Suppose that x=c is a critical point of fx then, If f 'x>0 to the left of…

Q: Find the curvature and radius of curvature of the plane curve at the given value of x. y =e-x/4, x =…

A: The given curve y=e-x4  ,  x=8

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

A: Given: z=x2+y2

Q: Find equations of the normal and osculating planes of the curve of intersection of the parabolic…

A:

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: A point moves along the intersection of the elliptic paraboloid z = 10x? + 3y² and the plane y = 1.…

A:

Q: 15. y= 2x +3 at x = 27

A:

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: A point moves along the intersection of the elliptic paraboloid z = 6r + 7y and the plane y = 2. At…

A: Given: A point moves along the intersection of the elliptic paraboloid z = 6x2 + 7y2 and the plane y…

Q: A point moves along the intersection of the elliptic paraboloid z = 2x? + 7y² and the planex = 4. At…

A:

Q: 3) Find the radius of curvature for the parametric curve x = e-t cost , y = e-t sin t.

A:

Q: Let r (t,t,t) be a curve in 3-dimensional space having unit tangent and norma V2 vectors u and n.…

A: We will use formula of curvature of a curve to solve it.

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

A:

Q: A curve C is defined as the intersection of the surfaces x^2+y^2=2 and z=x^2 . Find the curvature of…

A: We are given 2 surfaces in the 3D (three - dimension). We will use the definition of the curvature…

Q: verify Stokes § = (a%-y)i - yz'i over the uppea hazf SOD Face Of the sphere =1 bounded by the

A: Given that,  F→=(2x-y)i→-yz2j→-y2zk→ To verify Stoke's theorem: ∫CF→·dr→=∬Scurl F→·n^dS Here C is…

Q: Find the radius of curvature of 6y = x3 at the point (2,). %3D

A:

Q: Show that the circular helix r(t) = (a cos t, a sin t, bt), where a and b are positive constants,…

A: The equation of the given circular helix is rt=acost, asint, bt where a and b are positive…