Explanation is given below

Question

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 2021-05-19

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

asked 2021-05-21

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