Limits

When to Use

Use this skill when working on limits problems in real analysis.

Decision Tree

1. Direct Substitution

   • Try plugging in the value directly
   • If you get a determinate form, that's the answer

2. Indeterminate Form? (0/0, inf/inf)

   • Try algebraic manipulation (factor, rationalize)
   • Try L'Hopital's rule: sympy_compute.py diff on numerator/denominator

3. Squeeze Theorem

   • If bounded: find g(x) <= f(x) <= h(x) where lim g = lim h