Common techniques in evaluating limits are:
Find the limit:
Substituting directly:
Using the product rule,
Find the limit
Factoring and simplifying,
(Note that had you substituted t=2 directly in the original expression, you would have obtained a zero in both the numerator and denominator)
Multiplying both the numerator and the denominator by the conjugate of the numerator, , yields
You can see that the graph of f(x) approaches 3 as x approaches 0. Thus, the .
(Note that substituting 0 directly into the original expression would have produced a 0 in both numerator and denominator).
You notice that as x approaching 3 from the right, the graph of f(x) goes higher and higher, and that as x approaching 3 from the left, the graph of f(x) goes lower and lower. Therefore,
is undefined.