Let C be the space curve with the parametrization r(t) = (cost, sint, In (cost)) for - < t < 4. (a) Find the unit tangent vector T(t) of C at the point (1,0,0). (b) Find the unit normal vector N(t) of Cat (1,0,0). (c) Find the curvature of Cat (1,0,0).

Q: Find the point where the tangent line to the curve 7(?) = (V? +3,ln(?² +3),t) at (2, In 4,1) 5. %3D…

A:

Q: Find an equation of the tangent plane to the parametric surface R(u, v) = ((u - sin u) cos v, (1 -…

A:

Q: Consider the Parametric curve {x=t^3+ 2t^2+t y=t^2−7t+10 (a) It seems to have anxintercept at…

A:

Q: What is the unit tangent vector to the curve r(t)=⟨cost, sint, et⟩ at the point where t=0?

A: Given:          r(t)=cost,sint,et at t=0           r→(0)=cos(0),sin(0),e0          r→(0)=1,0,1…

Q: Find the unit tangent vector to the curve defined by r(t) = (4 cos(t), 4 sin(t), 2 sin²(t)) π at t =…

A:

Q: Eliminate the and write an equation of- carve in part (a) Sobely in cartesian coordinates x, y (e)…

A: As asked we shall solve only part (d) and (e).We have to eliminate the variable t and write the…

Q: t-) For each surface below, find the normal vector and equation of the tangent plane at the given…

A: Use definition of tangent plane and norman vector.  According to guidelins, we solve only first 3…

Q: The position vector of a particle is (a) Find the length of the curve for 1≤t≤4 (b) Find parametric…

A:

Q: Consider the function f(r, y) = e=² sin( q² + y²) (a) ) Compute the gradient of f. (b) 1 ) Find the…

A: Given fx,y=e-xsinx2+y2

Q: Q4 (a) Given a cylinder x' +y² = 1 and a plane x +z = 1. (i) Find a vector-valued function r(t) that…

A: we have,  A cylinder x2+y2=1 and a plane x+z=1 i x2+y2=1x2+y2=cos2t+sin2tx2+y2=cost2+sint2⇒x=cost,…

Q: (1 point) Find the curvature (t) of the curve r(t) = (4 sin t)i + (4 sin t)j + (5 cost) k

A: we will find the required solution.

Q: r(t) = (4+t)i+(9+ln(cos t))k, -pi/2 < t < pi/2 Find principal unit  normal vector N for the curve…

A:

Q: Consider the following vector function. - (46, ½-12², 1²) r(t): (a) Find the unit tangent and unit…

A:

Q: Consider the curve r(t) = (e' sin(2t), e' cos(2t), 2e*). (a) (b) (c) Find the osculating plane of…

A: Solution: The curve is r→t=etsin2t,etcos2t,2et

Q: Consider the curve C defined by (x; y) = r(t), where r(t) = (t; (1+t)/t; (1-t^2)/t) ; t > 0: (a)…

A:

Q: Find k (curvature) and t (torsion) for curve C represented by F(t)=(e^t,-e^t,(2t)^1/2)

A:

Q: (b) Find the curvature and the radius of curvature of the curve r (t) = e'i+e-tj+ tk at t = 0.

A: The given problem is to find the curvature and radius of curvature of the given vector curve.