Evaluating Limits

Most limits are easy — just plug in the value. The trouble is the 0/0 case, where plugging in gives an indeterminate dead end. Three algebraic tools rescue you: FACTOR and cancel, RATIONALIZE with a conjugate, or — when the two sides of the point simply disagree — report that the limit doesn't exist. The art of evaluating limits is recognizing which trap you've hit and pulling out the right tool. Each one trades the indeterminate form for a cleaner expression whose limit you can read off.