benchmarks.wiki

benchmarks.wiki / Public workspace

MMLU-Pro / 7974 / Let L^1[0,2] be the space of all the Lebesgue integrable functions on the…

Problem

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

question

Let L^1[0,2] be the space of all the Lebesgue integrable functions on the interval [0,2], and C[0,2] be the space of all the continuous functions on the interval [0,2]. Suppose H=L^1[0,2], and X=C[0,2]. For any f\in L^1[0,2], define operator T as (Tf)(x)=∫0xf(t)dt(Tf)(x)=\int_0^x f(t)dt. For the linear operator T from H to X, what is the norm of T? For the linear operator T from H to H, what is the norm of T? Return the answers of two questions as a list. For example, if the norm for the first question is 2, the second is 3, then return [2,3].
Plain-text mathematical notation (without MathML)
Let L^1[0,2] be the space of all the Lebesgue integrable functions on the interval [0,2], and C[0,2] be the space of all the continuous functions on the interval [0,2]. Suppose H=L^1[0,2], and X=C[0,2]. For any f\in L^1[0,2], define operator T as (Tf)(x)=∫₀^(x)f(t)dt. For the linear operator T from H to X, what is the norm of T? For the linear operator T from H to H, what is the norm of T? Return the answers of two questions as a list. For example, if the norm for the first question is 2, the second is 3, then return [2,3].
Original LaTeX notation
Let L^1[0,2] be the space of all the Lebesgue integrable functions on the interval [0,2], and C[0,2] be the space of all the continuous functions on the interval [0,2]. Suppose H=L^1[0,2], and X=C[0,2]. For any f\in L^1[0,2], define operator T as $(Tf)(x)=\int_0^x f(t)dt$. For the linear operator T from H to X, what is the norm of T? For the linear operator T from H to H, what is the norm of T? Return the answers of two questions as a list. For example, if the norm for the first question is 2, the second is 3, then return [2,3].

category

math

options

  1. [1, 2]
  2. [3, 1]
  3. [0.5, 1.5]
  4. [1, 3]
  5. [3, 2]
  6. [1, 4]
  7. [2, 2]
  8. [2, 3]
  9. [2, 1]
  10. [2.5, 2.5]

src

theoremQA-Math

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
7974
task_id
26a28f7f-97aa-5427-8a68-e24731b3c527
task_key
default--test--7974
task_revision_id
1
config / split
default / test

Official source

initial import