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anonymous

  • 5 years ago

How do you check the continuity of a multivariable function in a region bounded by two or more curves in the xy plane?

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  1. anonymous
    • 5 years ago
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    If the limit exists on every point of the function

  2. anonymous
    • 5 years ago
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    It's kinda hard to show that a limit exists with multivariables since we can approach any point in the function in infinity ways

  3. anonymous
    • 5 years ago
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    Everything that we used in single variables carries over like the squeeze theorem

  4. anonymous
    • 5 years ago
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    ok so i want to check the continuity of (x^4+4y^2) in the region bounded by y=x^2 and y=2x, which is continuous obviously, shouldn't there be a more concrete method to do the same for more complex functions

  5. anonymous
    • 5 years ago
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    The function is going to be continuous on all points in a polynomial. Unless you have have a function that is devided by the variables like in \[xy ^{2}/ x ^{2} + y ^{4} \] in this case the function is not continuous at (0,0) because \[\lim_{(x,y) \rightarrow (0,0)} x*y ^{2}/x ^{2}+ y ^{4} \] does not exists

  6. anonymous
    • 5 years ago
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    but for functions which are discontinuous at more than one point, or for trigonometric functions with infinite discontinuities, how can you say that a function is continuous in a region or not??

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