![]() Need some help studying? Check out this sample of Kaplan’s Rapid Review Live. If you have an idea about which colleges you want to go to, check out their websites or call the admissions office to find their particular rules regarding AP scores. Many colleges and universities will give you college credit for a score of 3 or higher, but some require a 4 or a 5. Estimate the value of the following limits. Your results will be placed into one of the following categories, reported on a five-point scale (relative to receiving college credit or advanced placement): Cisnero, AP CALCULUS BC CHAPTER 1 NOTES 3. After a bit of a wait, your composite score will arrive. ![]() The multiple-choice part is handled by a machine, while qualified readers-current and former calculus teachers and professors-grade your responses to Section II. When your three-plus hours of testing are up, your exam is sent away for grading. By finding two functions that are bounded by a third function, we can use the Squeeze Theorem to show that the limit of the first function is bounded by the limits of the other two functions. ![]() You should not spend too much time on any one problem. The Squeeze Theorem is a powerful tool for determining the limit of a function as it approaches a particular value. Therefore, you should answer every question, even if you have to guess.įor the Free Response section, all problems are given equal weight, but the individual parts of a particular problem are not necessarily given equal weight. No points are awarded for unanswered questions. no points are deducted for wrong answers. Here again, the theorem cannot be used, since the “inside” function has no limit as x approaches 0.Scores are based on the number of questions answered correctly. Limits You should be able to calculate limits algebraically or to estimate them from a graph or from a table of data. There is no way to work around the discontinuity. (This is the “outside” f, which is not continuous here.) This time, the limiting value, 2, is approached from both sides. Now as we approach 0 from both sides approached from both sides. To clarify this a little more, let’s look at a similar problem suggested by Sondra Edwards on the Facebook site: Consider this similar function: So we need to find the value of f as its argument approaches. But, notice that as x approaches 0 from both sides, the limit 2 is approached from the left (from below). Since f is not continuous at 2, the theorem cannot be used. ![]() Given the graph of a function f, shown at the left, what is ? In this form the limit is obviously 3.Įxample 2: The second example is also based on a graph. Although we cannot be certain, it appears that. Therefore, as f approaches 1 from the leftĪnother approach is to try to write the equation of f. However, on closer examination, we see that is always less than 1, so is approaching 1 from the left (or from below). Īt first glance it appears that as x approaches zero, approaches 1 and the limit does not exist since f is not continuous at 1, so the theorem cannot be used. Students were given the graph at the right and asked to find. Let’s look at some.Įxample 1:The first example is from the 2016 BC International exam, question 88. This does not mean that the limits necessarily do not exist, rather that we need to find some other way of determining them. The problem is that in the examples one or the other of the hypotheses (continuity or the existence of ) is not met. The theorem that we would like to apply in these cases is this: Recently, a number of questions about the limit of composite functions have been discussed on the AP Calculus Community bulletin board and also on the AP Calc TEACHERS – AB/BC Facebook page.
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