114 f(x, y) = (xy²-1 y-1 tion f(x, y) at the point (1,1), where (x, y) = (1,1) (x, y) = (1,1)
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- At what points (x, y, z) in space are the functions continuous? a. ƒ(x, y, z) = x2 + y2 - 2z2 b. ƒ(x, y, z) = 2x2 + y2 - 1Examine the continuity of f(x,y) at the origin, where a) F(x,y) = ( 3yx^2/y^2+2x4) , x,y!=0,0 =0, x,y=0,0 b) If x increases at a rate of 6cm/sec at the instant x=5cm and y=2cm, at what rate y must be changing inorder that the function 3xy-2xy^2 shall be neither increasing nor decreasingDetermine two functions, defined on the interval ( − ∞ , ∞ ) , whose Wronskian is given by W ( f 1 , f 2 ) = e 2 x . Are the functions that you found linearly independent on ( − ∞ , ∞ ) ? How do you know?