Find the value of k, for which $f(x) =\left\{\begin{array}{1 1}\frac{\sqrt{1+kx}-\sqrt{1-kx}}{x}, & if\;-1\leq x<0\\\frac{2x+1}{x-1}, & if\;0\leq x<1\end{array}\right.$ is continuous at x=0.

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(Note: This question has been split into 2 questions) This question appeared in 65-1,65-2 and 65-3 versions of the paper in 2013.