## Calculus (3rd Edition)

$$\kappa(t)=\frac{e^t}{\left(1+e^{2t}\right)^{3 / 2}},$$ $$\kappa(3)= \frac{e^3}{\left(1+e^{6}\right)^{3 / 2}},$$
We have $$\kappa(t)=\frac{\left|f^{\prime \prime}(t)\right|}{\left(1+f^{\prime}(t)^{2}\right)^{3 / 2}}=\frac{e^t}{\left(1+e^{2t}\right)^{3 / 2}},$$ and hence $$\kappa(3)= \frac{e^3}{\left(1+e^{6}\right)^{3 / 2}},$$