Evaluate each limit. If the limit does not exist, say so but also state if
Factor the numerator and denominator. If you can cancel out an
, then the limit exists. If not, then it DNE.
You could factor the denominator. Or you could multiply the top and bottom by the conjugate of
in the denominator will not cancel out. This means that there is a vertical asymptote at . How can we determine if the asymptote approaches or as from the left?
Choose a value that is to left of
, and evaluate. Note: we only need to determine if each term is positive or negative. Choose :
This is a limit
. That means we are looking at end behavior. Is there a horizontal asymptote, or do the y-values approach or ?
Consider only the terms with the highest power in the numerator and the denominator. Also consider their coefficients, and their signs.