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Question

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 2021-06-06

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

(a) \(f(x,y) = xy. c(t) = (cost,sint). 0 \leq t \leq 2 \pi\)

(a) \(f(x,y) = xy. c(t) = (cost,sint). 0 \leq t \leq 2 \pi\)

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 2021-03-20

The graph of y = f(x) contains the point (0,2), \(\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}={\frac{{-{x}}}{{{y}{e}^{{{x}^{{2}}}}}}}\), and f(x) is greater than 0 for all x, then f(x)=

A) \(\displaystyle{3}+{e}^{{-{x}^{{2}}}}\)

B) \(\displaystyle\sqrt{{{3}}}+{e}^{{-{x}}}\)

C) \(\displaystyle{1}+{e}^{{-{x}}}\)

D) \(\displaystyle\sqrt{{{3}+{e}^{{-{x}^{{2}}}}}}\)

E) \(\displaystyle\sqrt{{{3}+{e}^{{{x}^{{2}}}}}}\)

A) \(\displaystyle{3}+{e}^{{-{x}^{{2}}}}\)

B) \(\displaystyle\sqrt{{{3}}}+{e}^{{-{x}}}\)

C) \(\displaystyle{1}+{e}^{{-{x}}}\)

D) \(\displaystyle\sqrt{{{3}+{e}^{{-{x}^{{2}}}}}}\)

E) \(\displaystyle\sqrt{{{3}+{e}^{{{x}^{{2}}}}}}\)