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MMLU-Pro / 8754 / For every positive real number x, let …

Problem

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

question

For every positive real number xx, let g(x)=limr→0((x+1)r+1−xr+1)1/rg(x)=\lim _{r \rightarrow 0}((x+1)^{r+1}-x^{r+1})^{1/r}. What is the limit of g(x)/xg(x)/x as xx goes to infinity?
Plain-text mathematical notation (without MathML)
For every positive real number x, let g(x)=lim_(r→0)((x+1)^(r+1)−x^(r+1))^(1/r). What is the limit of g(x)/x as x goes to infinity?
Original LaTeX notation
For every positive real number $x$, let $g(x)=\lim _{r \rightarrow 0}((x+1)^{r+1}-x^{r+1})^{1/r}$. What is the limit of $g(x)/x$ as $x$ goes to infinity?

category

math

options

  1. 2
  2. Infinity
  3. 3.1415926
  4. 1
  5. 0
  6. 1.6180339
  7. 1.4142135
  8. 1.7320508
  9. 2.7182818
  10. 3.1415927

src

theoremQA-Math

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Source and history

upstream_id / Original problem ID
8754
task_id
e14ff8b0-f4e1-5b89-8180-303602fc7dd6
task_key
default--test--8754
task_revision_id
1
config / split
default / test

Official source

initial import