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Recent questions in Parametric equations

Find the maximum rate of change of f at the given point and the direction in which it occurs. $$\displaystyle{f{{\left({x},{y},{z}\right)}}}=\sqrt{{{x}^{{2}}+{y}^{{2}}+{z}^{{2}}}},\ {\left({9},{7},-{2}\right)}$$ maximum rate of change = direction vector =

Wanda Kane 2021-12-20 Answered

Find two unit vectors orthogonal to both $$\displaystyle{j}-{k}$$ and $$\displaystyle{i}+{j}$$.

Julia White 2021-12-20 Answered

What is the difference between f(-x) and -f(x)? What is the difference between $$\displaystyle{f{{\left(-{x}\right)}}}\ {\quad\text{and}\quad}\ -{f{{\left({x}\right)}}}$$ in terms of their graphs?

Sandra Allison 2021-12-16 Answered

How do you find parametric equations for the tangent line to the curve with the given parametric equations $$\displaystyle{x}={7}{t}^{{2}}-{4}$$ and $$\displaystyle{y}={7}{t}^{{2}}+{4}$$ and $$\displaystyle{z}={6}{t}+{5}$$ and $$\displaystyle{\left({3},{11},{11}\right)}$$?

Mabel Breault 2021-12-15 Answered

Find parametric equations for the path a particle that moves along the circle $$\displaystyle{x}^{{{2}}}+{\left({y}-{1}\right)}^{{{2}}}={4}$$ Find parametric equations for the path a particle that moves along the circle $$\displaystyle{x}^{{{2}}}+{\left({y}-{1}\right)}^{{{2}}}={4}$$. In the manner describe a) One around clockwise starting at (2,1) b) Three times around counterclockwise starting at (2,1) c) halfway around counterclockwise starting at (0,3)

Charles Kingsley 2021-12-15 Answered

Find the maximum and minimum values attained by the function f along the path $$\displaystyle{c}{\left({t}\right)}$$. $$\displaystyle{\left({a}\right)}{f{{\left({x},{y}\right)}}}={x}{y};{c}{\left({t}\right)}={\left({\cos{{\left({t}\right)}}},{\sin{{\left({t}\right)}}}\right)};{0}\le{t}\le{2}\pi$$ maximum value__________ minimum value__________ (b) $$\displaystyle{f{{\left({x},{y}\right)}}}={x}^{{{2}}}+{y}^{{{2}}};{c}{\left({t}\right)}={\left({\cos{{\left({t}\right)}}},{8}{\sin{{\left({t}\right)}}}\right)};{0}\le{t}\le{2}\pi$$ maximum value__________ minimum value__________

Margie Marx 2021-12-14 Answered

Find the maximum rate of change of f at the given point and the direction in which it occurs. $$\displaystyle{f{{\left({x},{y}\right)}}}={4}{y}\sqrt{{{x}}},\ {\left({4},{9}\right)}$$ maximum rate of change = direction vector =

David Lewis 2021-12-11 Answered

Find the domain of the vector-valued functions: (a) $$\displaystyle\vec{{{r}}}{\left({t}\right)}={\left\langle{t}^{{-{1}}},{\left({t}+{1}\right)}^{{-{1}}},{{\sin}^{{-{1}}}{\left({t}\right)}}\right\rangle}$$ (b) $$\displaystyle\vec{{{r}}}{\left({t}\right)}={\left\langle\sqrt{{{8}-{t}^{{{3}}}}},{I}{n}{\left({t}\right)},{e}^{{\sqrt{{{t}}}}}\right\rangle}$$

Kelly Nelson 2021-12-08 Answered

Find the domain of the vector-valued function $$\displaystyle{r}{\left({t}\right)}={F}{\left({t}\right)}\times{G}{\left({t}\right)}$$, where $$\displaystyle{F}{\left({t}\right)}={\sin{{t}}}{i}+{\cos{{t}}}{j},{G}{\left({t}\right)}={\sin{{t}}}{j}+{\cos{{t}}}{k}$$

Russell Gillen 2021-12-07 Answered

Suppose parametric equations for the line segment between $$\displaystyle{6},\ {7}{)}$$ and $$\displaystyle{\left({4},\ {5}\right)}$$ have the form: $\begin{cases}x(t) =a= bt \\ y(t)=c+dt \end{cases}$ If the parametric curve starts at $$\displaystyle{\left({6},\ {7}\right)}$$ when $$\displaystyle{t}={0}$$ and ends at $$\displaystyle{\left({4},\ {5}\right)}$$ at $$\displaystyle{t}={1}$$, then find $$\displaystyle{a},\ {b},\ {c}$$ and d.

Anne Wacker 2021-12-07 Answered