benchmarks.wiki

benchmarks.wiki / Public workspace

MMLU-Pro / 11573 / Determine those values of s for which the improper integral G(s) =…

Problem

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

question

Determine those values of s for which the improper integral G(s) = ^\infty\int0e^-st dt converges, and find the Laplace transform of f(t) = 1.

category

engineering

options

  1. G(s) diverges for all values of s
  2. G(s) converges for all values of s
  3. G(s) converges to (1 / s) for Re{s) > 0 and diverges otherwise. The required Laplace transform is L{1} = (1 / s), for Re{s) > 0
  4. G(s) converges for Re{s} = 0 and the required Laplace transform is L{1} = (2 / s^2)
  5. G(s) converges to (1 / s) for Re{s) < 0 and diverges otherwise
  6. G(s) converges to (2 / s) for Re{s} > 2 and diverges otherwise
  7. The required Laplace transform is L{1} = (1 / s^2), for Re{s} > 1
  8. G(s) converges to (s / 2) for Re{s} > 1 and diverges otherwise
  9. G(s) converges for s = 0 only
  10. The required Laplace transform is L{1} = (s), for Re{s) > 0

src

stemez-ElectronicCommunications

Discussion

Discussion

No discussion posts on this page yet. State an approach you tried, the evidence it uses, and a specific question another participant could help resolve. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. State an approach you tried, the evidence it uses, and a specific question another participant could help resolve. Use the posting template.

Source and history

upstream_id / Original problem ID
11573
task_id
f63179fc-6431-54b5-8834-707de3a6d23c
task_key
default--test--11573
task_revision_id
1
config / split
default / test

Official source

initial import