1.04 Algebraic Limits

Pre-Work:

1) Watch & Note Brightstorm’s “Evaluating Limits Algebraically (Part I)” videos:

•    Concept, Problem 1, Optional:  Problem 2, Problem 3

REMINDER: Bright Storm Log-in Information:

                           Username: af

                           Password: apcalculus

2) Copy the following NOTES and watch the corresponding videos:

• The standard technique that should always be attempted first is by using the fact that most functions are continuous (it is not undefined/denominator does not equal zero) and therefore to evaluate a limit, you must simply substitute in the value of x that the limit is evaluating.

• The standard technique of evaluating a limit by substitution doesn’t work when you end up with an undefined (meaning the denominator is equal to zero) or indeterminate limit (meaning both numerator and denominator are equal to zero at the same time). If this is the case, additional algebraic manipulation is needed. Also, don’t forget if you end up with a limit where you have 0/#, the limit is just zero in this case! 

     (i)          A technique that can be used if your function is not continuous at that x-value is factoring the numerator and denominator and cancelling like factors then substituting in the limit value. This technique is used when both the numerator and denominator are polynomials.Examples: Concept, Problem 1

    (ii)         If you cannot use continuity and the function contains a complex fraction, then try simplifying the complex fraction and cancelling any terms if necessary. This technique is used whenever there is a complex fraction within the function. Example: Problem 2

    (iii)               If you cannot use continuity and the function contains a radical in the DENOMINATOR. To simplify, multiply by the conjugate of the denominator in both the numerator and denominator.  Example: the conjugate of squareroot(x+3)-5 is squareroot(x+3)+5. Example :Problem 3

3) Copy and complete the attached Pre-Quiz (see attached file below) in your notebook.

4) Submit your pre-work in class or Google Classroom..