Mathematics I / Limits
Practice question · Multiple choice

The form 0/00/0 does not mean a limit fails to exist. What does it actually indicate?

Hints
  1. Evaluate lim⁡x→0sin⁡xx\lim_{x\to 0} \frac{\sin x}{x}, then lim⁡x→0xx2\lim_{x\to 0} \frac{x}{x^{2}}.
  2. Both are 0/00/0. Do they agree?
Show the answer

A. That the limit is indeterminate, so more work is needed

Why

Indeterminate means undecided, not undefined. Every derivative is a 0/00/0 limit, so treating the form as failure would abolish differential calculus.

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