Check whether the function values grow without bound as x approaches a point or infinity
Evaluate one-sided limits separately when approaching a finite value
Determine if the function approaches positive infinity or negative infinity
Use algebraic simplification to reveal dominant terms
Factor and cancel common terms when possible
Compare highest-degree terms for rational functions
Use leading coefficients and powers to identify end behavior
Analyze vertical asymptotes caused by zero denominators
Examine sign changes near points where the function is undefined
Apply limit laws when they help isolate unbounded parts
Use substitution only after confirming it does not create indeterminate forms
Check behavior from the left and right independently
Identify whether the limit does not exist because it diverges to infinity
Confirm infinite limits by testing values closer to the target point
Use graph behavior to verify unbounded growth or decay