Identify the function and the point the variable approaches
Substitute the value directly
If the result is an indeterminate form, simplify the expression
Factor and cancel common terms
Rationalize if square roots are involved
Combine fractions to get a common denominator
Use trigonometric identities if needed
Apply standard limit laws
Use known special limits
Evaluate one-sided limits if necessary
Check for continuity at the point
Use L’Hôpital’s rule for indeterminate forms if allowed
Use algebraic manipulation to rewrite the expression
Consider the behavior as the variable approaches infinity
Verify the final value from both sides when appropriate