http://www.intmath.com/differentiation/1-limits-and-differentiation.php |

http://www.wyzant.com/resources/lessons/math/calculus/limits/continuity |

http://www.tutorvista.com/content/math/discontinuity/ |

http://www.wyzant.com/resources/lessons/math/calculus/limits/continuity |

http://www.cwladis.com/math301/limitsgraphically.php |

3.We evaluate limits numerically by typing in the given function into out y= screen in our graphing calculator. Then, pressing the graph button and then hitting the trace button and we put in the number that we given in the table and repeat for all the others. On the left side of the table the number should increase from out to inner and on the right side of the table the number should increase out to inner. Then, you write out the number that is the middle or what the numbers are approaching and that number will become the limit. After, that you just write it as limit notation. We evaluate limits graphically by putting your finger on a spot to the left and to the right of where you want to evaluate the limit. If your fingers meet up then that y-value will be you limit. If your fingers do not meet up, the limit does not exist. The possible reasons for why the limit does not exist is because different values from the left and right, unbounded behavior, and oscillating behavior.We can evaluate limits algebraically by using three different methods. The first method, is substitution which is the easiest way to go about and we should always try to see if we get a numerical value, #/0(undefined= LIMIT DNE because unbounded behavior),and 0/#(limit is zero). If we ever get 0/0 when using the substitution method that means it is indeterminate, which means not yet determined and we must use another method. The substitution method means you take the number limit is approaching and plug it anytime you see "x". The second method, is factoring we use this method when the substitution method gives us 0/0 and the numerator or denominator are factorable. When using the factoring method we factor the numerator and denominator and cancel common terms to remove the zero(hole) in the denominator and then we use direct substitution method to get the limit. The last method is the conjugate method, we use this when the substitution method gives us 0/0 and the numerator or the demoniator are not factorable. We evaluate the limit using the conjugate method by first multiplying the top and bottom by the conjugate of the numerator or denominator(we use the conjugate of the numerator/denominator depending wherever the radical is). Then we simplify by foiling(you don't multiply the non-conjugate part because you want things to cancel) and then things will cancel and then we use the substitution method.

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