Substitute the value directly into the function
Simplify the expression algebraically if direct substitution gives an indeterminate form
Factor and cancel common terms
Rationalize numerator or denominator if radicals are involved
Combine fractions to a common denominator
Use standard limit laws
Apply special trig limits when needed
Use one-sided limits if the function behaves differently from each side
Check for discontinuities, holes, or asymptotes
Use L’Hôpital’s Rule for indeterminate forms when allowed
Rewrite the expression to a simpler equivalent form
Evaluate the limit from the left and from the right
Confirm the final result matches the behavior of the graph or table of values