Reflection 1

One thing that I grasped from this week was the “Strategies” that were given to us.
They are:
1) Factor and cancel
2) Rationalize (for square roots)
3) Graph or chart
Example: Factor and cancel
Lim as x approaches 2 X^2 – 7x + 10/x^2 – 4
-First you must factor, and you get: (x – 5) (x – 2)/(x – 2) (x + 2)
-Now you cancel the values from the numerator and denominator that are the same:
Leaving you with (x – 5)/(x + 2)
-Now plug in your x value (2 because it is the limit as x approaches 2) and you get -3/4.
Example: Rationalizing
Lim as x approaches 25 5 – sq. rt. (x)/ 25 – x
-When rationalizing, you must multiply the top and bottom by the conjugate, which in this problem is 5 + sq.rt. (x).
-After doing this, you get: 25 – x/(25 – x) (5 + sq.rt. (x))
-Now cancel the 25 – x’s and you are left with 1/5 + sq.rt. (x)
-Now plug in x, and you get 1/10.

Graph or chart
When possible, you can use your calculator to either graph out the equation and find the limit visually or make the chart we learned at the beginning of the year, and you can find the limit that way.

THE KEY TO THIS is just practicing. All of the problems we will have will be similar, you just have to practice them until you get a complete understanding of how to work them out, not to mention practice will help you to do the process much faster.