Find the limit:

Substituting directly:

Find the limit:

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)

Find the limit

Multiplying both the numerator and the denominator by the conjugate of the numerator,

, yields

(Note that substituting 0 directly into the original expression would have produced a 0 in both numerator and denominator).

Find the limit

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).

Find the limit

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.