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