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(a) Find radius of curvature of curve:

x2+ xy + y2= 4 at point (–2, 0)


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
The earth is not homogeneous body.It is a dynamic and differentiated body. explain
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;
Prove or disprove any metric defined on X(#0) induces a topology on X
Prove or disprove any metric defined on X(#0) induces a topology on X
Prove or disprove any metric defined on X(#0) induces a topology on X
Prove or disprove every topological space is metrizible
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
Prove that the boundary of a subset A of a metric space X is always a closed set
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