2. Describe each of the following with a parametrization. Be sure to indicate the possible values for parameter your (a) Traversing the circle of radius 3 centered at the point (5,7) twice counter-clockwise (b) Staying at the point (10,25) for all time

Q: ind the equation for the tangent plane to the surface z = In(6x2 +9y2 + 1) at the point (0,0, 0).…

A:

Q: To illustrate thefact that the numbers we get for length do not depend on the waywe parametrize our…

A:

Q: Find the equation for the tangent plane at the point Po = (1,2, 2) on the surface x + 4y2 + 22 = 25.…

A: Equation of the Surface x2+4y2+2z2=25 point 1,2,2

Q: find the radius of curvature at any point on parabola y2=4ax

A: Given:  y2 = 4axTo find: The radius of curvature at any point on the given parabola. Formula used:…

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 radius of curvature at any point on parabola y2=4ax

A:

Q: Find a parametrization of the vertical line passing through the point (9, 5, 0) using t = z as a…

A:

Q: Find the arc length of the curve C from the origin to the point (1/2, 1/6, 1) , where C' is the…

A: Given equations are z2=2x and 3y=xz. Now multiplying z2=2x with z:  z3=2xzz3=6y

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: Find the EXACT area inside the closed loop produced from the following parametric curve. Show ALL…

A: The area is the amount of space occupied by a two-dimensional figure. In other words, it is the…

Q: Find a parametrization for the curve described below. the line segment with endpoints (4,4) and…

A: Given,  A line segment with endpoints 4, 4  and  6, 1  We have to find the parametrization of the…

Q: Find the equation of the tangent plane to the following surface at the given point. 4y cos (3ar 2)…

A: Given equation of surface and point is

Q: Find an equation of the tangent plane to the surface given by z² – 2x2 – 2y? = 12 at the point (1,…

A:

Q: Find the equation of the tangent plane at the point T(1,1,4) of the sphere (x – 1)2 + (y – 2)² + (z…

A:

Q: find the areas of surfaces generated by revolving the curves about the given axes

A:

Q: Parametrize the osculating circle to y = √x at x = 4.

A: Given that the osculating circle  y = x

Q: Find a parametrization for the curve described below. the line segment with endpoints (1, – 4) and…

A: Given:   Endpoint : ( 1 , -4) and ( -2 , -7)

Q: Give two different parametrizations of the line through (4, 1) withslope 2.

A: Solution:GivenA point(4,1) with slope 2Formula:Equation of the line at (x1,y1)y-y1=m(x-x1)

Q: Find a parametrization for the curve described below. the line segment with endpoints (- 2,4) and (-…

A:

Q: Is the below statement True or False? The parametrization for a given curve is unique.

A: No. Parametrization of a curve is not unique. For example y = x2 can be written as (t,t2) or…

Q: Write the parametrization for a circle with each of the following conditions: Centered at the…

A: Given that,   The Centered at the origin; initial point (t=0) is (-7,0)and one full circle is traced…

Q: Q2 Find the radius of curvature of y5 =x at the point (x,v.). Hence, show that the radius of %3D…

A: The curve is y5=x3

Q: Find the equation of the tangent plane to the paraboloid z = 2x2 +y? at the point (1,2,6). Select…

A:

Q: Find a parametrization for the following curve. a.) The circle centered at (2,1) of radius 3.

A:

Q: Find the area of the surface generated by revolving the curve about each given axis. x= 5t, y- 9t,…

A:

Q: Express the following curves parametrically, including the interval for the parameter. 2.) 2.) A…

A:

Q: Find a parametrization of the osculating circle for the parabola y = x2 when x = 1

A: It is given that, y = x2.The parametrization is, r (t) = <t, t2>That implies,

Q: whose x-coordinates are equally ine with parabolic runout conner

A: Given as.     python code :

Q: For KEIRT and TEIR construct Co-Curve Y: IR→IR³ with constant Curvature K and constant torsion T

A:

Q: 3. Find the radius and center of curvature of the parabola y=x²-4x+4 at any point (x,y)on the curve.

A:

Q: 2r find the moment with respect to the wavic of the area hounded by the parabola v - Av-172 and v

A:

Q: Find an equation for the tangent plane to the surface 2° – ay? = 0 at the point (27, 1, 3).

A:

Q: Evaluate F. dī where F = , and C' is the circle of - counterclockwise direction.

A:

Q: Find a parametrization of the circle of radius 6 in the XY-plane, centered at the origin, oriented…

A:

Q: Use Stoker Cur theorem to evaluate. IF - ds S Where F= of radius I with x ] +ya³k ands is the +yx³k…

A: Given That  ∬Curl F →·dS→ F→=yi-xj+yx3k To Find: evaluate  ∬Curl F →·dS→  using strokes theorem

Q: Find an equation of the tangent plane to the given surface at the specified point. 3Vy Z = VY, (-1,…

A:

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

A:

Q: 2 Find the point onthe curve y=Jx that is. the point (4,0). minimum distance from a

A:

Q: Find the equation of the tangent plane to the sphere x² + y2 + z² = 1 at the point (1/ V3, 1/V3, 1/…

A:

Q: Find an equation of the tangent plane to the given surface za² + y² +1 at (1,1,3).

A: Given equation of the surface is  z=x2+y2+1 We have to find the tangent plane of the given surface…

Q: 9) Sketch x = indieate the onientatiba of the 2t°, y = 3t, -4sts4 aud with %3D Curve an arow,

A:

Q: To illustrate thefact that the numbers we get for length do not depend on the waywe parametrize our…

A:

Q: (a) Prove that curves a, ß: I → R² are congruent if k̟ = Kg and they have the same speed.

A: Part (a):   If any two continuous function defined on the interval I, and the two curves are…

Q: Sketch the reglon enclosed by the given curves. Dedde whether to iIntegrate with respect to or y.…

A:

Q: Find a parametrization of the osculating circle for the parabola y= X sequar when x=1

A: The given equation of parabola is y = x2.We are asked to find the equation of osculating circle for…

Q: Find a parametrization for the curve described below. the line segment with endpoints (4,1) and…

A: The line segments between  (xo , yo)  and  ( x1, y1)  can be expressed as:x(t) = (1 − t)xo + tx1…

Q: )2. Find the paramehic from the cune check whether the cure is a repulor cuwe. AGo reparametije the…

A: Note: According to our guideline we will answer the first question as the exact one is not…

Q: Determine the orthogonal trajectories of the family of circles (equation below) that is tangent to…

A:

Q: - Show that the distance r from the origin O to the point P(Coshu,Sinhu) - on the hyperbola x-y 1 is…

A:

Q: Find the area of the surface generated by revolving the curve about each given axis. x = 6t, y = 9t,…

A: Here,  we need to find the surface generated by revolving the curve x=6t, y=9t, 0≤t≤3, about each…