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13 Nov 2019
1. Let f(x, y) be a function of two variables, and consider the usual notation that we have been using to study the differentiation at a point (zo, yo) We can say that f(x, y) is differentiable at (xo, yo) when there are two constants a and b such that lim (The point is that this is a slightly more abstract definition of differentiability that doesn't presuppose the value of the derivative.) Prove thatf(x, y) has both partial derivatives at xo, Vo), that the only value of a that could work in this equation is a--(x0, y0), and likewise that the only value of b that could work is b- (xo, yo). (Hint: As a special case of the 2-dimensional limit, you are allowed to let 0 and take the limit just in Az. for instance.) of
1. Let f(x, y) be a function of two variables, and consider the usual notation that we have been using to study the differentiation at a point (zo, yo) We can say that f(x, y) is differentiable at (xo, yo) when there are two constants a and b such that lim (The point is that this is a slightly more abstract definition of differentiability that doesn't presuppose the value of the derivative.) Prove thatf(x, y) has both partial derivatives at xo, Vo), that the only value of a that could work in this equation is a--(x0, y0), and likewise that the only value of b that could work is b- (xo, yo). (Hint: As a special case of the 2-dimensional limit, you are allowed to let 0 and take the limit just in Az. for instance.) of
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Sixta KovacekLv2
30 Oct 2019