MATH 2D Study Guide - Final Guide: Tangent Space, Maxima And Minima, Partial Derivative
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MATH 2D Full Course Notes
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Find the limit for the following multivariable functions or to show the limit does not exist: (a) (b) lim (x,y) (1,1) 3x2 cos(x + y) x2 + 3y2 lim (x,y) (0,0) 3x2 cos(x + y) x2 + 3y2 (c) lim (x,y) (0,0) Page 2: let f (x, y) =(cid:112)x2 + 4y2 be a function of two variables. (a) calculate f. Page 3 (c) use the equation for the tangent plane to give an approximate value of. Page 4: let f be a function of two variables de ned as f (x, y) = xy2 x2 + y2 . (a) what is the natural domain of f? (b) consider another function f de ned as. F (x, y) = if (x, y) (cid:54)= (0, 0) if (x, y) = (0, 0). Show f is a continuous function on r2. (state your reason clearly. )
