15. Find the radius of curvature at 0 = -n of the parametric equations x = 3(0 + cos 0), y = 3(1 – cos 0). -

Q: Find the parametric equations of normal line to the surface given by f(x,y) = tan Vx2 + y² at the…

A:

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

A:

Q: Find the radius of curvature of the parabola y² = 4px at (0, 0).

A: Given that the parabola y² = 4px  To Find the radius of curvature of the given parabola at (0,0).…

Q: Q1. Find the curvature of the line whose parametric equations are given as: x = -2+t, y =3+ 2t, z…

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Q: 4. Find the parametric equations for the tangent line to the curve of intersection of the y? z1…

A:

Q: Find the radius of curvature at 0 = t of the parametric equations x = 3(0 + cos 0), y = 3(1 – cos…

A: To find the radius of curvature, first find out dxdθ and d2xdθ2. x=3θ+cos θdxdθ=31-sin θd2xdθ2=-3cos…

Q: 2. Write an integral expression to represent the length of the path described by the parametric…

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Q: 5. Eliminate the parameter to find a Cartesian equation of the following curves. et (a) x = vt+1, y…

A: Eliminate parameter t.

Q: 2. Given the parametric equations: x = t + sin t,y = t- cost, findand

A: Solution...

Q: Find the equation for the principal curvatures, the differential equation of the lines of curvature,…

A: Given equation is 2z=x2a+y2b2p=2xa, where ∂z∂x=p and 2q=2yb, q=∂z∂ya=xp and b=yq2z=x2xp+y2yq2z=px+qy

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

A:

Q: III. Find the parametric equations of normal line to the surface given by f(x, y) = tan 2 V + y? at…

A:

Q: 15. Find the radius of curvature at 0 = ÷n of the parametric equations x = 3(0 + cos 0), y = 3(1 —…

A: Given two parametric equations, x=3(θ+cosθ),y=3(1-cosθ) To find the radius of curvature at θ=π3

Q: DETERMINE THE APEA UNDER THE PARA HETRIC CURVE GIUEN DY THE FOLLO WING PARAMETRIC EQUATIONS. x=2 (6…

A: We have to find the area under the curve.

Q: (7.5.0)- Find an equation of the tangent plane to the surface of z = sin(x – 2y) at the point %3D

A: Given F(x, y, z)=z-sin(x-2y) ∂∂xF(x, y, z)=∂∂x(z-sin(x-2y))=-cos(x-2y)∂∂yF(x, y,…

Q: In three dimensions, the cylinder x? + z2 – 10x – 6z – 2 = 0 has radius k i +tj+ and the axis line…

A: Radius =6  r(t)= (5+6cos(thetha))i+tj+(3+6sin(thetha)k

Q: 4. Consider the surface S parametrized by R(u, v) = (uv, sin u, cos v). Find an equation for %3D the…

A: The given curve S is parametrized by: R→(u,v)=uv,sin u,cos v Now, to find the equation of the…

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

A: Sol

Q: 4 Find the curvature k of the plane curve y = x +- at x = 1. K =

A: Given curve is , y= x + 4x  at x=1

Q: 8. Find the positive constant a(> 0) so that the parametric x = at, y = -t? is a solution to y =…

A:

Q: 7. The curve at right is given by the parametric equations t2 z = v2t. x = In t, y = Find its length…

A: Given that, x=lnt,y=t22 and z=2t. That is, r→t=lnt,t22 ,2t. It is known that, the length of the…

Q: A particle is moving in space with position function R(t) = (cos(4t), sin(4t),5 – 3t) Find the…

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Q: 5. Find the general equation of the circle of curvature of the parametric equation X= ;y=+√6(t+1);…

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Q: 3. A curve has parametric equations r = sin(3t) and y = cos(t) where t takes all real %3D values. dy…

A:

Q: 8. Find a Cartesian equation for the surface whose spherical equation is p= 2 sin() sin(0).

A: Solve the following

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

A:

Q: 1. Find the points on the parabola y 8x at which the radius of 125 curvature is 16

A:

Q: 29. Find parametric equations for the tangent line to the cur ve of intersection of the paraboloid z…

A: Given paraboloid is z=x2+y2 ellipsoid is x2+4y2+z2=9 and the point (1,-1,2) find the parametric…

Q: 1. Evaluate the length of the curve defined by the parametric equations x = cost, y=sint, z…

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

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Q: 1. Find an equation of the tangent plane to the surface of z = sin(x – 2y) at the point (7.5.0).

A: First partially differentiate the function with respect to x,y and z and then proceed as shown…

Q: 4. Solve for the critical points of the given parametric equation: x = t³ – 1; y = t² + t

A:

Q: 8. Solve for the critical points of the parametric equations x = t3 – 1,y = t² +t %3D

A: The answer is found in step-2.

Q: 4) Find the critical points of the parametric equations x = 5 – In t y = t + Int

A:

Q: Find parametric equations for the tangent line to the curve of intersection of the cylinders x? +² =…

A: Here finds the parametric equation for the tangent line to the curve of intersection.   where the…

Q: 7. Find an equation of the tangent plane to the given surface at the specified point. cos(x –…

A:

Q: 7) Find the curvature of y = e* at the point (0, 1). Then find the equation of the osculating circle…

A: Given curve, y=ex

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

A:

Q: A curve is defined by the parametric equations z (t) = at and y (t) = bt, where a and b are…

A: Given,  We have  xt = at   and yt = bt  ;  where a and b are constants.  We have to find the length…

Q: Find the equation for the principal curvatures, the differential equation of the lines of curvature,…

A:

Q: 2. Find a set of parametric equations for a particle that oscillates on the line y = 6x – 5 between…

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Q: 8. Solve for the critical points of the parametric equations x = t - 1,y = t² +t

A: To find the critical points of parametric curve x(t)=t2-1, y(t)=t2+t

Q: 30. Find parametric equations for the tangent line to the curve of intersection of the cone z = x +…

A:

Q: The length of the path describe by the parametric equations, x=(1/3)t^3 and y=(1/2)t^2, where 0≤t≤1,…

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Q: If I have a pair of parametric equations  x=20cos(t) and y=10sin(t)  How can I increase the speed…

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Q: 1. Find the tangent to the curve given by the parametric equations: X = 1/t; y= VE e-t

A: Appliaction of derivative problem