asked 2021-01-28

Given the vector \(r(t) = { \cos T, \sin T, \ln ( \cos T) }\) and point (1, 0, 0) find vectors T, N and B at that point.

Vector T is the unit tangent vector, so the derivative r(t) is needed.

Vector N is the normal unit vector, and the equation for it uses the derivative of T(t). \(\)

The B vector is the binormal vector, which is a crossproduct of T and N.

asked 2021-03-02

asked 2021-05-03

asked 2021-03-08

(a) Find the velocity vector, speed, and acceleration vector of the object.

(b) Evaluate the velocity vector and acceleration vector of the object at the given value of \(\displaystyle{t}=\sqrt{{3}}\)

asked 2021-03-02

asked 2020-11-30

Consider \(\displaystyle{V}={\cos{{\left({x}\right)}}},{\sin{{\left({x}\right)}}}\) a subspace of the vector space of continuous functions and a linear transformation \(\displaystyle{T}:{V}\rightarrow{V}\) where \(\displaystyle{T}{\left({f}\right)}={f{{\left({0}\right)}}}\times{\cos{{\left({x}\right)}}}−{f{{\left(π{2}\right)}}}\times{\sin{{\left({x}\right)}}}.\)

Find the matrix of T with respect to the basis \(\displaystyle{\cos{{\left({x}\right)}}}+{\sin{{\left({x}\right)}}},{\cos{{\left({x}\right)}}}−{\sin{{\left({x}\right)}}}\) and determine if T is an isomorphism.

asked 2021-05-01

eliptic cylinder

circular paraboloid

hyperbolic paraboloid

plane

circular cylinder