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

step by step solution :

step   1   :

1.1     4 = 22

(4)3 = (22)3 = 26

equation at the end of step   1   :

  ((23) • 26)2

step   2   :

equation at the end of step   2   :

  (23 • 26)2

step   3   :

final result :

  218

ya

no oblique asymptote

step-by-step explanation:

to find the oblique asymptote of f(x)

here numerator has degree 1 and denomintor degree 2

degree of numerator < degree of denominator

hence there is no oblique asymptote

when the degree of the denominator > that of the numerator, we saw that the value in the denominator got so much bigger, so quickly,   giving us a horizontal asymptote of the x-axis. or we can write

f(x) = a polynomial of x + a proper fraction.

in this case only we have oblique asymptotes but not when numerator has less degree.

hi do you need an answer for your question?

step-by-step explanation: