Use the important limit lim (1+1/x) x = e.
x→∞
Then lim (1+3k/(x-k)) k = lim {(1+3k/(x-k)) [(x-k)/3k]} (3kx/(x-k)).
And lim (1+3k/(x-k)) [(x-k)/3k] = e.
Then the original formula = lime (3kx/(x-k))
= Lime (3k) = 27
k=ln3
~~~~~~~~~~~~~~~~~
dy/dx=(dy/dt)/(dx/dt)
=[2t/( 1+t^2)]/[ 1- 1/( 1+t^2)]
=2t/t^2
= 2/ ton
Then d 2y/dx 2
=(d(dy/dx)/dt)/(dx/dt)
=(-2/t^2)/[ 1- 1/( 1+t^2)]
=-2( 1+t^2)/t^4