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Problem

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

question

Suppose $E \subset(0,2 \pi) is a measurable set. \left\{\xi_n ight\}$ is an arbitrary sequence of real numbers. If the Lebesgue measure of E is 2, what is limnightarrow∞∫Ecos2(nx+ξn)dx\lim _{n ightarrow \infty} \int_E \cos ^2 (n x+\xi_n ) dx? Return the numeric.
Plain-text mathematical notation (without MathML)
Suppose $E \subset(0,2 \pi) is a measurable set. \left\{\xi_n
ight\}$ is an arbitrary sequence of real numbers. If the Lebesgue measure of E is 2, what is lim_(nightarrow∞)∫_(E)cos²(nx+ξ_(n))dx? Return the numeric.
Original LaTeX notation
Suppose $E \subset(0,2 \pi) is a measurable set. \left\{\xi_n
ight\}$ is an arbitrary sequence of real numbers. If the Lebesgue measure of E is 2, what is $\lim _{n 
ightarrow \infty} \int_E \cos ^2 (n x+\xi_n ) dx$? Return the numeric.

category

math

options

  1. $\frac{\sqrt{2}}{2}$
  2. 0.0
  3. $\pi$
  4. 1.5
  5. 1.0
  6. 3.0
  7. 2.0
  8. 2.5
  9. 0.5
  10. $\frac{\pi}{2}$

src

theoremQA-Math

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Source and history

upstream_id / Original problem ID
8520
task_id
9d73a9e8-657d-5684-8028-4d2c54bae229
task_key
default--test--8520
task_revision_id
1
config / split
default / test

Official source

initial import