Skill: limits
Limits Tutor Help
A one-page recap of the four limit methods and the mistakes to avoid, plus a way to ask a tutor for a worked explanation.
1 Quick recap
The essentials on one page before you ask for help.
Limit methods
Substitute → factor → conjugate → special
(x² − k²)/(x − k) → 2k · (√(x+a) − b)/(x − c) → 1/(2b) · sin(kx)/(mx) → k/m
(x² − k²)/(x − k) → 2k · (√(x+a) − b)/(x − c) → 1/(2b) · sin(kx)/(mx) → k/m
0/0 is never the answer — it is the signal to simplify. The two-sided limit exists only when the one-sided limits agree.
Stuck? Check these first
- Try substitution first. If the denominator is nonzero, you are done.
- Factor before you panic: difference of squares (x − k)(x + k) cancels the hole.
- With roots, multiply by the conjugate — the x − c you need will appear.
- The limit cares about the approach, never the value at x₀.
2 Ask a tutor
Tell us what you are stuck on. A tutor will follow up with a worked explanation.
3 Keep going
While you wait, review the lesson or drill practice problems.