A vector-valued function r(t) with its defining parametric equations is given by the following

asked 2021-09-02

\(\displaystyle{r}{\left({t}\right)}={\left({\sin{{t}}}\right)}{i}+{\left({1}+{\cos{{t}}}\right)}{j}+{\left({4}{t}\right)}^{{{2}}}{k}\) vector -valued fuction defined in the from is given.

\(\displaystyle{\int_{{0}}^{{\frac{{\pi}}{{{2}}}}}}{r}{\left({t}\right)}{\left.{d}{t}\right.}\) calculate its integral

\(\displaystyle{\int_{{0}}^{{\frac{{\pi}}{{{2}}}}}}{r}{\left({t}\right)}{\left.{d}{t}\right.}\) calculate its integral

asked 2021-11-25

Represent the plane curve by a vector-valued function.

y=x+1

r(t)=(t)i+(t+1)j

y=x+1

r(t)=(t)i+(t+1)j

asked 2021-11-26

Domains Find the domain of the following vector-valued function.

\(\displaystyle{r}{\left({t}\right)}={\frac{{{2}}}{{{t}-{1}}}}{i}+{\frac{{{3}}}{{{t}+{2}}}}{j}\)

\(\displaystyle{r}{\left({t}\right)}={\frac{{{2}}}{{{t}-{1}}}}{i}+{\frac{{{3}}}{{{t}+{2}}}}{j}\)

asked 2021-11-27

Domains Find the domain of the following vector-valued function.

\(\displaystyle{r}{\left({t}\right)}=\sqrt{{{4}-{t}^{{2}}}}{i}+\sqrt{{{t}}}{j}-{\frac{{{2}}}{{\sqrt{{{1}+{t}}}}}}{k}\)

\(\displaystyle{r}{\left({t}\right)}=\sqrt{{{4}-{t}^{{2}}}}{i}+\sqrt{{{t}}}{j}-{\frac{{{2}}}{{\sqrt{{{1}+{t}}}}}}{k}\)

asked 2021-09-06

\(P(-8,-2,-2), Q(-3,-9,-4)\)

Represent the line segment from P to Q by a set of parametric equations

asked 2021-08-29

Writing a Vector-Valued function in exercise , represent the line segment from P to Q by a vector-valued function and by a set of parametric equations:

P(-2,5,-3),Q(-1,4,9)

P(-2,5,-3),Q(-1,4,9)

asked 2021-11-28

Determine the interval(s) on which the vector-valued function is continuous

\(\displaystyle{r}{\left({t}\right)}={2}{e}^{{-{t}}}{i}+{e}^{{-{t}}}{j}+{\ln{{\left({t}-{1}\right)}}}{k}\)

\(\displaystyle{r}{\left({t}\right)}={2}{e}^{{-{t}}}{i}+{e}^{{-{t}}}{j}+{\ln{{\left({t}-{1}\right)}}}{k}\)