Answer
$$\frac{1}{\sqrt{2}}$$
Work Step by Step
We find:
$\frac{\left|y^{\prime \prime}x^{\prime} -x^{\prime \prime} y^{\prime} \right|}{\left(y^{\prime 2}+x^{\prime 2}\right)^{3 / 2}}= \kappa$
$1=x^{\prime}(t) \quad -1 / t^{2} =y^{\prime}(t)$
$0=x^{\prime \prime}(t) \quad 2 / t^{3}=y^{\prime \prime}(t)$
$1=x^{\prime}(1) \quad -1=y^{\prime}(1) \quad 0=x^{\prime \prime}(1) \quad 2=y^{\prime \prime}(1)$
$\kappa=\frac{|1(2)-(-1)(0)|}{(1+1)^{3 / 2}}=\frac{2}{2 \sqrt{2}}=\frac{1}{\sqrt2}$
