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: on numerator/denominator 3. Squeeze Theorem - If bounded: find g(x) <= f(x) <= h(x) where lim g = lim h - Verify bounds with 4. Epsilon-Delta Proof - For rigorous proof: set up |f(x) - L| < epsilon - Find delta in terms of epsilon - Verify with Tool Commands Sympy Limit Sympy…