For those who enrolled in the Beacon Program at Suffolk County Community College, I have been informed that I should be receiving a spreadsheet from them with your student ID's by mid June. Once the course is complete, I will be able to enter your final grade for the course through Suffolk. I will be posting more information at a later date regarding transcript requests from Suffolk. LIMITS at INFINITY So far, we have been checking what the limit of a function is as a function approaches a specific x-value. Now we are going to find the limits for a function as x goes to either positive or negative infinity. The basic strategy is to determine where the biggest power of x is in a function. If you understand this, you can basically just LOOK at the problem and give the correct answer. There are NOT a lot of calculations that need to be done, so do not OVER-COMPLICATE the process. There is one of 3 possibilities if a limit exists. A) The biggest power of x is in the numerator. The limit will be either plus or minus infinity depending on the sign of the function. B) The biggest power of x is in the denominator. The limit will be 0. C) The highest power of x is the same in both the numerator and the denominator. The limit will be the ratio of the lead coefficients of the highest powers. The sign will be either positive or negative depending on the value of x being plugged in (- x if going to -infinity or +x if going to + infinity) and the signs of the lead power coefficients. This might sound familiar to you. If you think back to when we were graphing rational functions and had to determine if there was a horizontal asymptote (HA), we had to check to see whether the highest power in the function was on top (= no HA), bottom (HA of y=0) or equal on top and bottom (HA of y= ratio of lead coefficients). It is also possible that no limit exists if the function is not approaching a single value as x goes to +/- infinity. Videos: This first video shows the mathematics behind the process. The intro part explains the concept well and I recommend you watch that piece. When it demonstrates finding the limit of a rational function (fraction) and starts dividing everything by the largest power of x in the denominator, this is OVER-COMPLICATING how to solve the problem. Skip to where he gets to the final answer and then go back to the beginning and use my rule of finding the biggest power. You should be able to visually come up with the same answer without all the math that he shows. www.youtube.com/watch?v=lMJ_-rq71l4 Shows the short cuts - getting the answer by inspection. (Where is the biggest power.) www.khanacademy.org/math/ap-calculus-ab/ab-limits-new/ab-1-15/v/limits-at-positive-and-negative-infinity www.khanacademy.org/math/ap-calculus-ab/ab-limits-new/ab-1-15/v/more-limits-at-infinity www.youtube.com/watch?v=75xO9xy7TTQ www.youtube.com/watch?v=NmLljBAg82o Assignment due 6/12/20 - page 915: numbers 1 – 14, 20, 22, 24 Assignment due 6/17/20 - Review - two handouts A) Review sheet #8528 - omit problems 16 and 17 B) Review sheet of limits - problems 1-25
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