Are the functions in Exercises 1-6 continuous at all points the given regions? 1

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Are the functions in Exercises 1-6 continuous at all points the given regions? 1/x2 + y2 on the square -1 x 1, -1 y 1 1/x2 + y2 on the square 1 x 2, 1 y 2 y/x2 + y2 on the disk x2 + y2 1 esin x/cox y on the rectangle -pi/2 x pi/2, 0 y pi/4 tan(xy) on the square -2 x 2, -2 y 2 2x - y on the disk x2 + y2 4 In Exercises 7-11, find the limits of the functions f(x,y) as (x,y) rightarrow (0, 0). Assume that polynomials, exponentials, logarithmic, and trigonometric functions are continuous. f(x,y) = e-x-y f(x,y) = x2 + y2 f(x,y) = x/x2 + 1 f(x,y) = x + y/(sin y) + 2 f(x,y) = sin(x2 + y2)/x2 + y2 [Hint: limtrightarrow0 sin t/t = 1.]

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