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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


The real line with the usual topology is locally compact

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/ey 5) x+4ydy/dx = 0



State and prove contraction lemma
When do you say that a topological space is second countable ?Given an example of a second countable topological space
Prove that the property being a Hausdroff space is a topological and hereditary property

Give an example of seperable Hausdroff space which has a non seperable subspace


Prove that seperability is a topological property


Let (X,(tua)) be a space and ((X) infinity, (tau) infinity) its one point compactification .prove that ((X)infinity, (tau)infinity) is compact
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