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MMLU-Pro / 11501 / Use the Laplace transform of f(t) = e^kt,(1) where k is a complex constant of…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

Use the Laplace transform of f(t) = e^kt,(1) where k is a complex constant of the form k = Re{k} + i Im{k} with Re{k} the real part of k, Im{k} the imaginary part of k, and i \equiv \surd(- 1), to find the Laplace transforms of f(t) = cosh kt, sinh kt, cos kt, and sin kt.

category

engineering

options

  1. L{cosh kt} = [k / (s^2 - k^2)], L{sinh kt} = [s / (s^2 + k^2)], L{cos kt} = [k / (s^2 + k^2)], L{sin kt} = [s / (s^2 - k^2)]
  2. L{cosh kt} = [2s / (s^2 - k^2)], L{sinh kt} = [2k / (s^2 - k^2)], L{cos kt} = [2s / (s^2 + k^2)], L{sin kt} = [2k / (s^2 + k^2)]
  3. L{cosh kt} = [s / (s^2 + k^2)], L{sinh kt} = [k / (s^2 - k^2)], L{cos kt} = [s / (s^2 - k^2)], L{sin kt} = [k / (s^2 + k^2)]
  4. L{cosh kt} = [k / (s^2 + k^2)], L{sinh kt} = [s / (s^2 + k^2)], L{cos kt} = [k / (s^2 - k^2)], L{sin kt} = [s / (s^2 + k^2)]
  5. L{cosh kt} = [s / (s^2 - k^2)], L{sinh kt} = [2k / (s^2 + k^2)], L{cos kt} = [2s / (s^2 - k^2)], L{sin kt} = [s / (s^2 + 2k^2)]
  6. L{cosh kt} = [s / (s^2 + k^2)], L{sinh kt} = [k / (s^2 + k^2)], L{cos kt} = [s / (s^2 - k^2)], L{sin kt} = [k / (s^2 - k^2)]
  7. L{cosh kt} = [s / (s^2 + 2k^2)], L{sinh kt} = [k / (s^2 + 2k^2)], L{cos kt} = [s / (s^2 - 2k^2)], L{sin kt} = [k / (s^2 - 2k^2)]
  8. L{cosh kt} = [s / (s^2 - 2k^2)], L{sinh kt} = [k / (s^2 + 2k^2)], L{cos kt} = [s / (s^2 + 2k^2)], L{sin kt} = [k / (s^2 - 2k^2)]
  9. L{cosh kt} = [k / (s^2 + k^2)], L{sinh kt} = [s / (s^2 - k^2)], L{cos kt} = [s / (s^2 - k^2)], L{sin kt} = [k / (s^2 - k^2)]
  10. L{cosh kt} = [s / (s^2 - k^2)], L{sinh kt} = [k / (s^2 - k^2)], L{cos kt} = [s / (s^2 + k^2)], L{sin kt} = [k / (s^2 + k^2)]

src

stemez-ElectronicCommunications

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Source and history

upstream_id / Original problem ID
11501
task_id
b9185180-dec0-59c1-ab2c-6e13fd3c8f98
task_key
default--test--11501
task_revision_id
1
config / split
default / test

Official source

initial import