Differential Geometry | Topology

(a) Find radius of curvature of curve:

x^{2}+ xy + y^{2}= 4 at point (–2, 0)

Differential Geometry | Topology

Determine the unit tangent vector at the point (2,4,7) for the circle with parametric equations x=2u, y=u^2 +3 and z=2u^2 +5

Differential Geometry | Topology

The earth is not homogeneous body.It is a dynamic and differentiated body. explain

Differential Geometry | Topology

Define an operator T in End(F^2) by T(x,y)= (y,0) Let

U = {(x,0) | x in F}. Show that

U is invariant under T and T |U is the 0 operator on U;

U = {(x,0) | x in F}. Show that

U is invariant under T and T |U is the 0 operator on U;

Differential Geometry | Topology

Prove or disprove any metric defined on X(#0) induces a topology on X

Differential Geometry | Topology

Prove or disprove any metric defined on X(#0) induces a topology on X

Differential Geometry | Topology

Prove or disprove any metric defined on X(#0) induces a topology on X

Differential Geometry | Topology

Prove or disprove every topological space is metrizible

Differential Geometry | Topology

Let E be a Euclidian vector space, let (i,j) be its standard basis. Note C

the circle centered at the origin with radius a, where a is a real positive number. ⃗⃗

1. Let δ = (a cos as )i+(a sin as )j. Show that ([0, 2πa], δ) is a unit speed parametrization of C

the circle centered at the origin with radius a, where a is a real positive number. ⃗⃗

1. Let δ = (a cos as )i+(a sin as )j. Show that ([0, 2πa], δ) is a unit speed parametrization of C

Differential Geometry | Topology

Prove that the boundary of a subset A of a metric space X is always a closed set