Substitute the value directly if the function is continuous at that point
Simplify the expression algebraically if direct substitution gives an indeterminate form
Factor and cancel common terms
Rationalize the numerator or denominator if radicals are involved
Use a common denominator to combine fractions
Apply trigonometric identities for trig limits
Use special limit formulas when applicable
Apply L’Hôpital’s Rule for indeterminate forms when allowed
Use the squeeze theorem when the function is trapped between two others with the same limit
Evaluate one-sided limits separately if necessary
Check for infinite limits or vertical asymptotes
Use limit laws to break complex limits into simpler parts
Consider substitution for composite expressions
Use series expansions or approximations if appropriate
Confirm the result from both sides when the limit is two-sided