Find the value of `k ,` for which `f(x)={{(sqrt(1+k x)-\ sqrt(1-k x))/(x(2x+1)/(x-1\ ))\ \ ,\ \ \ \ \ \ \ "if",\ -1lt=x<0"if"\ 0lt=x<1` is continuous at `x=0`

Explanation

for continous function at any point p n

`implies`left hand side limit should be equal to the right hand side limit

`f(0)=(2x+1)/(x-1)`
`=1/-1=-1`
`lim(x->0) f(x)=((sqrt(1+kx)-sqrt(1-kx)))/x` multiply and devide by `(sqrt(1+kx)+sqrt(1-kx)`
`lim(x->0)f(x)=(2*k*x)/(x(sqrt(1+kx)+sqrt(1-kx))`
`implies` `2k/k=1`

Ans=
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