Differential Geometry | Topology Answers

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

a) Find the gradient of the curve at (2,-3)

b) what does your answer to part (a) tell you about the point (2,-3)

1. Find the smooth curve (C1) realizing the shortest distance between two given points in a plan (usual Euclidean R2).

Let p= sin t i + cost j + tk, What is |dp/dt|?

a.\\(\\sqrt(7)\\)

b.\\(\\sqrt(2)\\)

c.\\(\\sqrt(3)\\)

d.\\(\\sqrt(5)\\)

let r(t)= (e^kt cos t, e^kt sint) find the arc length of r starting at the point (1,0)

find the arc length of r(t)=(e t sin t , e t cos t ,e t)

Bob claims that he can map rectangle 1 to rectangle 2

Find the radius of curvature of follium decart x^3+y^3=3axy at the point (3a,3a)

find the radius of curvature at the point (1,1) of the folium x^3+y^3=2yx

Trace the curve (x/a)^2/3 + (x/a) ^2/3=1