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Lacey-May Snyder

Answered 2021-06-07
Author has **24706** answers

asked 2021-07-31

For each of the following, find the maximum and minimum values attained by the function f along the path c(t):

(a) \(\displaystyle{f{{\left({x},{y}\right)}}}={x}{y}.{c}{\left({t}\right)}={\left({\cos{{t}}},{\sin{{t}}}\right)}.{0}\leq{t}\leq{2}\pi\)

(a) \(\displaystyle{f{{\left({x},{y}\right)}}}={x}{y}.{c}{\left({t}\right)}={\left({\cos{{t}}},{\sin{{t}}}\right)}.{0}\leq{t}\leq{2}\pi\)

asked 2021-08-03

For each of the following, find the maximum and minimum values attained by the function f along the path c(t):

(b) \(\displaystyle{f{{\left({x},{y}\right)}}}={x}^{{2}}+{y}^{{2}}.{c}{\left({t}\right)}={\left({\cos{{t}}},{2}{\sin{{t}}}\right)}{.0}\leq{t}\leq{2}\pi\)

(b) \(\displaystyle{f{{\left({x},{y}\right)}}}={x}^{{2}}+{y}^{{2}}.{c}{\left({t}\right)}={\left({\cos{{t}}},{2}{\sin{{t}}}\right)}{.0}\leq{t}\leq{2}\pi\)

asked 2021-05-19

(b) \(f(x,y) = x^2 + y^2. c(t) = (\cos t, 2 \sin t).0 \leq t \leq 2 \pi\)

asked 2021-12-14

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__________

\(\displaystyle{\left({a}\right)}{f{{\left({x},{y}\right)}}}={x}{y};{c}{\left({t}\right)}={\left({\cos{{\left({t}\right)}}},{\sin{{\left({t}\right)}}}\right)};{0}\le{t}\le{2}\pi\)

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__________

asked 2021-05-21

Find the absolute maximum and absolute minimum values of f over the interval. \(f(x)=(\frac{4}{x})+\ln(x^{2}), 1\leq x\leq 4\)

asked 2021-12-09

Find the maximum and minimum values attained by the function falong the path \(\displaystyle{c}{\left({t}\right)}\).

\(\displaystyle{f{{\left({x},{y}\right)}}}={x}{y};\ {c}{\left({t}\right)}={\left({\cos{{\left({t}\right)}}},\ {\sin{{\left({t}\right)}}}\right)};\ {0}\le{t}\le{2}\pi\)

\(\displaystyle{f{{\left({x},{y}\right)}}}={x}{y};\ {c}{\left({t}\right)}={\left({\cos{{\left({t}\right)}}},\ {\sin{{\left({t}\right)}}}\right)};\ {0}\le{t}\le{2}\pi\)

asked 2021-12-02

Find the maximum and minimum values attained by the function falong the path \(\displaystyle{c}{\left({t}\right)}\).

\(\displaystyle{f{{\left({x},{y}\right)}}}={x}^{{2}}{y}^{{2}};\ {c}{\left({t}\right)}={\left({\cos{{\left({t}\right)}}},\ {3}{\sin{{\left({t}\right)}}}\right)};\ {0}\le{t}\le{2}\pi\)

\(\displaystyle{f{{\left({x},{y}\right)}}}={x}^{{2}}{y}^{{2}};\ {c}{\left({t}\right)}={\left({\cos{{\left({t}\right)}}},\ {3}{\sin{{\left({t}\right)}}}\right)};\ {0}\le{t}\le{2}\pi\)