LIMITS IN CALCULUS BC PLUS
LIMITS IN CALCULUS BC SERIES

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: You must also understand how and when to use each formula.įurthermore, there are tons of more specialized formulas that didn’t make it to this list.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. Memorizing a list of formulas will not guarantee you a high score on the exam. This list provides just the foundation for your study.

LIMITS IN CALCULUS BC SERIES

Below are some common Maclaurin series that are worth memorizing. If a function f is differentiable to all orders, then you can build its Taylor series centered at c as follows.Ī Taylor series centered at c = 0 is called a Maclaurin series. Just as in the ratio test, if the limit is > 1, then the series diverges. However, if the limit is > 1, then the series diverges. And in that case, the error bound for the nth partial sum is | a n+1|. If the series is alternating (i.e., the terms alternate in sign forever), then the series converges if and only if a n → 0 as n → ∞. The Intermediate Value Theorem (IVT) states that if a function f is continuous on a closed interval, and if L is any number between f( a) and f( b), then there must be a value x = c where a 1 and diverges if p ≤ 1. Instead, each limit problem may require different algebraic or trigonometric “tricks.” However, it helps to know L’Hospital’s Rule:Ī function f is continuous at a point x = a if: There are not a lot of formulas for computing limits. Integrals and Their Applications (AB and BC).

Derivatives and Their Applications (AB and BC).The formulas can be categorized into four Big Ideas. It might help to look through the following “Cram Sheets” first.

LIMITS IN CALCULUS BC PLUS

Moreover, if you plan to take the Calculus BC exam, then you will have to know every formula that could show up on the AB exam, plus a whole slew of additional formulas and concepts that are specific to the BC exam. There are a number of basic formulas from calculus that you need to memorize for the exam. Once you have mastered those fundamental topics of mathematics, you can then build your expertise in calculus. For a quick review check out the following helpful articles. The Basic Formulasįirst and foremost, you must be you must know arithmetic, algebra, and trigonometry inside-out. The tallest skyscrapers require a solid foundation in order to stand.

Limits in calculus bc