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MMLU-Pro / 4179 / Show that l'Hôpital's rule amounts to forming a Taylor expansion of both the…

Problem

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

question

Show that l'Hôpital's rule amounts to forming a Taylor expansion of both the numerator and the denominator. Evaluate the limit limx→0ln(1+x)−xx2 \lim _{x \rightarrow 0} \frac{\ln (1+x)-x}{x^2} both ways.
Plain-text mathematical notation (without MathML)
Show that l'Hôpital's rule amounts to forming a Taylor expansion of both the numerator and the denominator. Evaluate the limit
lim_(x→0)(ln(1+x)−x)/(x²)
both ways.
Original LaTeX notation
Show that l'Hôpital's rule amounts to forming a Taylor expansion of both the numerator and the denominator. Evaluate the limit
$$
\lim _{x \rightarrow 0} \frac{\ln (1+x)-x}{x^2}
$$
both ways.

category

chemistry

options

  1. 3/2
  2. 0
  3. -3/2
  4. 2
  5. 1/4
  6. 1
  7. -1
  8. -1/2
  9. 1/2
  10. -2

src

scibench-chemmc

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Source and history

upstream_id / Original problem ID
4179
task_id
58b6263a-d236-58f0-8797-93c85cbfa6f1
task_key
default--test--4179
task_revision_id
1
config / split
default / test

Official source

initial import