Differential Geometry | Topology Answers

The Euclidean space p² is metric space . Specially R^' (real line) R²( the complex plane) etc are metric .

Let X be a metric space ,then show that

(a) A subset F of X is closed iff F^c is open .

(b) A subset E of X is open iff E^c is closed .

Let the position vector of a stone at time,t be given as r(t)=cosh (t^2-1)I+ sinh(1-t)j+Bt^2k

Assume that the position vector is Normal to the acceleration vector.

Find the value of B at Time t=5seconds

A particle moves in space so that at time t its position is stated as x=2t+3, y=t²+3t, z=t³+2t² Find the components of its velocity and acceleration when t=1

Find the general solution of these differential equations.

3) dy/dx = cosx/y 4) dy/dx = 4x/e^y 5) x+4ydy/dx = 0