 User (login-registrate)
 Limits Evaluating limits Common techniques in evaluating limits are: substituting directly factoring and simplifying multiplying the numerator and denominator of a rational function by the conjugate of either the numerator or denominator using a graph or a table of values of the given function. 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.