find the Cerrvature of the Curve x:(0,1|R? defined by x(t)=14Cost, 1sint,o), where %3D is coostant 2

Q: Find the area of the surface obtained by rotating the given curve about the x-axis. - 10 10 cos (0),…

A: Find the derivatives with respect to θ

Q: Show that at any point (x,y) on the curve y=bex/a ,the length of the subtangent cosgant and the…

A:

Q: Determine the exact area between the x-axis and the curve defined parametrically by 2 x(t) = - +² t²…

A:

Q: Compute the arc length of the parametric curve given X=1/3t^3-t,y=t^2+3 From t=0 to t=3

A:

Q: The length of the curve defined parametrically by: x = e*cost, y = e' sint, 0 Sts is equal to:…

A:

Q: Given the xーxy+y? %3D 9 2. Curve 6. Find the coordinates of the POTnts on the Curve where the…

A:

Q: (b) Consider the curve C with parametirzation 7(t) = (5 cost, 5 sin t, 500), where 0 <t< 27. Let F =…

A: We have,

Q: Let C be the curve given by r(t) = (t cost,t sin t,t).(a) Show that C lies on the cone x 2 + y2 = z2

A: Consider the parametric equation of the curve C : rt=tcos t,t sin t, t. To show C lies on cone…

Q: Find the length of the curve x = e' cos(t), y = e' sin(t), 0 <t < r. Length =

A:

Q: Calculate F.dr, where C is the curve given by ti + 123+ tk, with t = [0, 1] and F(x, y, z) = 4xei +…

A:

Q: Compute f ds for the curve specified. f(x, y, z) = 2x2 + 8z, c(t) = (e*, t², t), 0 sts 1

A:

Q: Let C be the curve defined by 7(t) = (2+2 sin(t), 3 – 2 cos(t)) for 0 <t< L (e + 4z) dz + (2zye" +…

A:

Q: the detined b is Constant. Curiature a(t) =| 1 Cost, 1 sint, o of the curve d:laa)tR? where Find

A: We are given : α(t)=1rcos t,1rsin t,0 ⇒α'(t)=-1rsin t,1rcos t,0 Now, the Unit tangent Vector is :…

Q: Find the arc length of the curve x = t², y =t-, 0sts v2. 2.

A:

Q: How many points are there on the surface 2 dx+y such that the tangent plane to the surface is…

A: We have given the a=6,b=9,c=9 d=max(a,b,c)=max(6,9,9)=9 The given surface is f(x,y,z)=9x2+y2-z We…

Q: Find the point(s) on the surface z = xy + 1/x + 1/y at which the tangent plane is horizontal.

A: Given that: The surface  z = xy+1x +1y  .

Q: The length of the curve defined parametrically by: x = e*cost, y = e'sint,0 <t <, s equal to: Select…

A: tea

Q: Consider a new curve Č parametrized by r(t) = (cos t esint, sin t- cos t), 0 <t <I but with F still…

A:

Q: Find the moment of inertia, with respect to the line x=1, of the area enclosed by the loop of the…

A:

Q: Find the arc length of the curve on the given interval. Parametric Equations     x = √t, y = 3t − 1…

A: Given: Parametric Equations x = √t, y = 3t − 1 Interval 0 ≤ t ≤ 1

Q: Find the arc length of the parametric curve. x = e', y = e, = V2t; 0<t< 2 L

A:

Q: Find the length of the subtangent and subnormal of a point of the curve y=b sin (x/a)

A:

Q: Practice by Evaluating Fodr where, F(x, y) = e" (sin(y)î + cos(y)ĵ) C: is a smooth curve from (0,0)…

A:

Q: Consider the curve y = zy+1. What is the value of- dz at (0, 1)? None of the given choices

A: The solution for the above question is as shown below.

Q: where C is the curve r(t) = (sin(t), cos(t), sin(2t)), 0 ≤ t ≤ 2

A: Given C is the curve                        r(t)=sin(t), cos(t), sin(2t), 0≤t≤2π and…

Q: Compute f ds for the curve specified. f(x, y, z) = 2x? + 40z, c(t) = (5e", 5t2, 5t), 0sts 1 %3D

A: Use parametric to solve

Q: The length of the curve defined parametrically by: x = e'cost, y = eʻsint,0 <t <, is equal to:…

A: given parametric curve x=etcost     y=etsint

Q: Which type of surface does the curvex= cos(3t),y= sin(3t),z=t, lie on?

A:

Q: On the following Cartesian Plane, sketch a curve with the following properties: dy 0 on (-0, 0) and…

A: First understanding the meaning of mathematical equations then sketching the graph

Q: Consider the curve f(y) = sy + for 1 <y < 3. Find the arc length of the curve. 4y %3D

A: The length of the curve is given by                                                    L=∫abf'y2+1dy

Q: Can there be a curve satisfying the following conditions? d2y/dx2 is everywhere equal to zero and,…

A: To check: The curve satisfying the given condition or not.Explanation:

Q: Compute f ds for the curve specified. f(x, y, z) = x²z, r(t) = (3e*, 2/6t, 4e-t) for 0 sts1

A: Given:

Q: s) Evaluate the line itegral ( +2y + 2)dy – dz, where C is the arc of parabola z = 2+ y". from (2,0)…

A:

Q: Find the required x-value. For a x2-cu -curve with 27 degrees of freedom, find the X-value having…

A: Given data:Degree of freedom  =27 Area to the right  = 0.01

Q: Evaluate + 5x)dx + (ye* – 3y²)dy where C is the boundary of the curve given below. -2

A: Detailed explanation mentioned below

Q: What's a parameterized version of the curve given by y - 3 = x + sin x? A. y = -3t, x = y+ sin t…

A: The equation of the curve is y-3=x+sin x. That is, the equation can be rewritten as, y=x+sin x+3.

Q: Find the area of the closed region enclosed by the curve defined parametrically by x = 4 cos t, y =…

A:

Q: Find the arc length of the parameterized curve over the interval 1 ≤ t ≤ 2. x = t3 + 1 y = 2t9/2

A:

Q: The value of f. ydx + zdy + xdz where C is the curve x = y = z = 2t? from t = 0 to t = 1 is

A: Here we have to find the value of ∫cydx+zdy+xdz where C is the curve x=y=z=2t2 from t=0 to t=1.

Q: . Find SF dř where F(x,y,z) = (3y?e*, 6ye* -, 1+) and C is the curve F(t) = (sin t, ,2-) for 0 stsn.

A:

Q: Find the length of the curve C defined parametrically by C: r(t) = y(t) = e' sin t, 0<t<n e cost,…

A:

Q: Find the lenght of the curve y = x- tnx, 1+/dy 2. dx %3D %3D

A:

Q: s Find the exact slope of the tangent line to the parametric curve π t = x = 9 cos(t) y = 4 sin(t)…

A:

Q: b) Sketch the graph and find the points on the cardioid r=a(1+cos) at which tangent lines are…

A: Consider the equation of the cardioid, r=a1+cosθ The graph will be,

Q: Use Green's Theorem to evaluate / F · dř, where F = (Va + 6y, 3x + y9) C consists of the arc of the…

A:

Q: Consider the given curve: R(f) = (2 cos f, 12f +3,-2 sin f) Reparametrize the curve using arclength…

A:

Q: Let C be the part of the curve x? + y² = 1 with y 2 0, oriented counter- clockwise. Evaluate F. dr,…

A: