Substitute the value directly into the function
If the result is defined, that is the limit
If direct substitution gives an indeterminate form, simplify the expression
Factor and cancel common terms
Rationalize the numerator or denominator if needed
Use common denominators to combine fractions
Apply limit laws to split complex expressions into simpler parts
Evaluate one-sided limits if the function behaves differently from each side
Check for vertical asymptotes if the function grows without bound
Use special trigonometric limits when applicable
Apply L’Hôpital’s Rule for indeterminate forms if allowed
Use algebraic manipulation to rewrite the expression
For limits at infinity, compare highest-degree terms in rational functions
For piecewise functions, evaluate each relevant piece separately
Verify the left-hand and right-hand limits are equal for a two-sided limit
Confirm the final value matches the simplified expression near the target point