Substitute the value directly
Simplify algebraically if direct substitution gives an indeterminate form
Factor and cancel common terms
Rationalize expressions when square roots are involved
Find a common denominator for fractions
Use trigonometric identities for trig limits
Apply standard limit laws
Use the squeeze theorem when appropriate
Evaluate one-sided limits if needed
Check for vertical asymptotes and discontinuities
Use L’Hôpital’s rule for indeterminate forms when allowed
Rewrite expressions to match known limit forms
Use graphing or tables to estimate the limit
Verify the result by approaching from both sides
Confirm whether the limit exists or does not exist