Calculus › Section B · Limits › Topic B.5
Infinite limits and vertical asymptotes
Some limits fail in the most dramatic way: the function races off beyond any bound. Giving that behaviour its own language, and its own landmark, the vertical asymptote, turns 'no limit' into a precise description.
In this topic
- Failure with a shape
- Speaking infinity correctly
- Vertical asymptotes
- The rule, and why it works
- Worked example: signing the blow-up
- Worked example: hole versus asymptote
- Arithmetic around a blow-up
- A blow-up in the physical world
- Common mistakes to avoid
- Key takeaways
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