Limits of rational functions
The limit of a rational function at infinity containing roots (irrational expressions)
The limit of a rational function at a point containing irrational expressions, use of substitution
Evaluating the limit of a rational function containing irrational expressions using rationalization
The limit of a rational function at infinity containing roots (irrational expressions)
We use the same method we used to evaluate the limit of a rational function at infinity that is, isolate and cancel a common factor of x from both the numerator and denominator and than find the limit of the equivalent expression.
 Example:  Evaluate the limit
 Solution:
 Example:  Evaluate the limit
 Solution:
The limit of a rational function at a point containing irrational expressions, use of substitution
Use of the method of substitution to avoid the indeterminate form of an expression.
 Example:  Evaluate the limit
Solution:     Let substitute,   x + 1 =  y6,   then as  x ® 0  then   y ® 1,   therefore
 Example:  Evaluate the limit
Solution:     Let substitute,   xy12,   then as  x ® 1  then   y ® 1,   therefore
Evaluating the limit of a rational function containing irrational expressions using rationalization
To avoid the indeterminate form of the irrational expression we rationalize the numerator or the denominator as appropriate.
 Example:  Evaluate the limit
Solution:     Let rationalize the numerator,
 Example:  Evaluate the limit
Solution:     Let rationalize both the numerator and denominator,
Calculus contents B