Yahoo Answers: Answers and Comments for For what values of k is limx→∞(coshkx)/(sinh3x) finite? [Mathematics]
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From munnaam
enUS
Wed, 20 Feb 2019 17:00:20 +0000
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Yahoo Answers: Answers and Comments for For what values of k is limx→∞(coshkx)/(sinh3x) finite? [Mathematics]
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https://answers.yahoo.com/question/index?qid=20190220170020AAjEpyS
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From emira: sinh(kx) / cosh(3x) = [ e^(kx)  e^(kx) ] / [...
https://answers.yahoo.com/question/index?qid=20190220170020AAjEpyS
https://answers.yahoo.com/question/index?qid=20190220170020AAjEpyS
Wed, 20 Feb 2019 17:24:47 +0000
sinh(kx) / cosh(3x) = [ e^(kx)  e^(kx) ] / [ e^(3x) + e^(3x) ]
When x is large and assume k >= 0
sinh(kx) / cosh(3x) ≈ e^(kx) / e^(3x) = e^(x(k  3))
For sinh(kx) / cosh(3x) to be finite
e^(x(k  3)) is finite
==> k  3 <= 0
==> k <= 3
==> 0 <= k <= 3
Similarly, when x is large, and k <= 0
sinh(kx) / cosh(3x) ≈ e^(kx) / e^(3x) = e^(x(k  3))
e^(x(k  3)) is finite
==> k  3 <= 0
==> k + 3 >= 0
==> k >= 3
Combining both scenarios gives the range of k of [3, 3]