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ianmartin6080
ianmartin6080
25.02.2020 • 
Mathematics

To find the extreme values of a function f(x,y) on a curve xequals=x(t), yequals=y(t), treat f as a function of the single variable t and use the chain rule to find where df/dt is zero. As in any other single-variable case, the extreme values of f are then found among the values at the critical points (points where df/dt is zero or fails to exist), and endpoints of the parameter domain. Find the absolute maximum and minimum values of the following function on the given curves. Use the parametric equations xequals=2 cosine t2cost, yequals=2 sine t2sint. Functions: Curves:

a. f(x,y) equals= xplus+y i) The semicircle x2plus+y2equals=4, ygreater than or equals≥0
b. g(x,y) equals= xy ii) The quarter circle x2plus+y2equals=4, xgreater than or equals≥0, ygreater than or equals≥0 c. h(x,y) equals= 2x2plus+y2

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