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The limit command in Maple 2019 has been enhanced for the case of limits of quotients of multivariate functions:
Many such limits that could not be determined previously are now computable, including all of the following examples.
Returning ranges instead of undefined in the bivariate case
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Support for functions containing abs or radicals
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Why?
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| > | ![`assuming`([simplify(`/`(`*`(abs(y)), `*`(`^`(`*`(`^`(y, 2)), `/`(1, 2)))))], [real])](MultivariateLimits/MultivariateLimits_10.gif){kind=small} |
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| > | ![`assuming`([simplify(`/`(`*`(abs(y), `*`(`^`(2, `/`(1, 2)))), `*`(`^`(`*`(`^`(y, 2)), `/`(1, 2)))))], [real])](MultivariateLimits/MultivariateLimits_14.gif) |
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Support for functions in more than 2 variables
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Why?
| > | ![eval(f, [y = 0, z = 0])](MultivariateLimits/MultivariateLimits_25.gif){kind=small} |
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| > | ![eval(f, [y = 0, z = `+`(`*`(`^`(x, 4)), `-`(x))])](MultivariateLimits/MultivariateLimits_29.gif){kind=small} |
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Why?
| > | ![`assuming`([simplify(f)], [real])](MultivariateLimits/MultivariateLimits_36.gif){kind=small} |
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Why?
| > | ![eval(f, [y = 0, z = 0])](MultivariateLimits/MultivariateLimits_41.gif){kind=small} |
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| > | ![`assuming`([simplify(`/`(`*`(`^`(`*`(`^`(x, 4)), `/`(1, 2))), `*`(`^`(x, 2))))], [real])](MultivariateLimits/MultivariateLimits_43.gif) |
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| > | ![eval(f, [y = x, z = x])](MultivariateLimits/MultivariateLimits_45.gif){kind=small} |
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| > | ![`assuming`([simplify(`+`(`/`(`*`(`/`(1, 3), `*`(`^`(3, `/`(1, 2)), `*`(`^`(`*`(`^`(x, 4)), `/`(1, 2))))), `*`(`^`(x, 2)))))], [real])](MultivariateLimits/MultivariateLimits_47.gif) |
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Why?
| > | ![eval(f, [y = 0, z = 0])](MultivariateLimits/MultivariateLimits_54.gif){kind=small} |
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| > | ![eval(f, [y = x, z = x])](MultivariateLimits/MultivariateLimits_56.gif){kind=small} |
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