5. Consider the function (x, y) = (0,0), f(x, y) = (x, y) = (0,0). (a)...
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5. Consider the function (x, y) = (0,0), f(x, y) = (x, y) = (0,0). (a) For any real number m, define the (single-variable!) function 9m(x) = f(x, mx). (This is the restriction of f to the line y=mx.) Show that every 9m is a continuous function of x, even at x = 0. +y² (b) Does your answer to part (a) imply that f is continuous at (0,0)? Why or why not? (c) For any real number m, define h(x) = f(x, mx²). What is lim-ohm (x)? Explain what this has to do with part (b). 5. Consider the function (x, y) = (0,0), f(x, y) = (x, y) = (0,0). (a) For any real number m, define the (single-variable!) function 9m(x) = f(x, mx). (This is the restriction of f to the line y=mx.) Show that every 9m is a continuous function of x, even at x = 0. +y² (b) Does your answer to part (a) imply that f is continuous at (0,0)? Why or why not? (c) For any real number m, define h(x) = f(x, mx²). What is lim-ohm (x)? Explain what this has to do with part (b).
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a b c Fx y Imx fix mx lim x40 Harying Fxy xma xxmx xy xy lim y Here x fday A... View the full answer
Related Book For
Differential Equations and Linear Algebra
ISBN: 978-0131860612
2nd edition
Authors: Jerry Farlow, James E. Hall, Jean Marie McDill, Beverly H. West
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