91Ó°ÊÓ

Find the curvature of each of the vector-valued functions defined in Exercises 39–44.

$\mathit{r}\left(t\right)=\left(t\sin t,t\cos t,2t\right)$

Evaluate the integral:

Evaluate the limits in Exercises 42–45.

$\underset{t→\mathrm{π}}{lim}(\sin t,\cos t,sect)$

Find the curvature of each of the vector-valued functions defined in Exercises 39–44.

$\mathit{r}\left(t\right)=\left(t\sin t,t\cos t,\mathrm{Î\pm }t\right),\mathrm{where}\mathrm{Î\pm }\mathrm{is}\mathrm{a}\mathrm{constant}$

Evaluate the limits in Exercises 42–45.

$\underset{t→1^{-}}{lim}(\ln t,\frac{e^t-1}{t-1},e^t)$

Evaluate the integral:

Find the curvature of each of the vector-valued functions defined in Exercises 39–44.

$\mathit{r}\left(t\right)=\left(\sin t,\cos t,\cosh t\right)$

Use the given velocity vectors v(t)=r'(t) and initial positions din Exercises 45-48 to find the position function r(t).

Use the given velocity vectors $v\left(t\right)=r\text{'}\left(t\right)$and initial positions in exercise to find the position function $r\left(t\right)$.

Evaluate the limits in Exercises 42–45.

$\underset{t→0^{+}}{lim}(\frac{\sin t}{t},\frac{1-\cos t}{t},{(1+\frac{1}{t})}^t)$