How to Calculate Limits
What is Limits?
Limit describes value function approaches as input approaches some value: lim(x→a) f(x) = L. Foundation of calculus.
Step-by-Step Guide
- 1Input function and point
- 2Calculate limit by substitution, factoring, L'Hôpital's rule, or numeric approximation
- 3Results show limit value
Worked Examples
Input
lim(x→2) (x²-4)/(x-2)
Result
= lim(x→2) (x+2) = 4 (factor to remove discontinuity)
Common Mistakes to Avoid
- ✕Direct substitution when undefined (0/0)
- ✕Not checking left and right limits
Frequently Asked Questions
When does limit not exist?
If left/right limits differ, oscillates, or diverges to infinity.
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