Know your Limits
This is the value that a function (or sequence) "approaches" as the input (or index) approaches some constant.
What is a limit?
This type of function has no domain restriction and can be defined as either even or odd by the degree of the leading term.
What is a polynomial?
These are the three major types of discontinuity addressed in calculus.
What are removable, jump, and infinite?
This famous mathematician is generally perceived as the father of calculus.
Who is Gottfried Wilhelm Leibniz?
This is the term for a triangle with three unequal length sides.
What is scalene?
This is the limit as you approach 0 of sin(x) / x.
What is 1?
This function is useful for modeling the growth of bacterial colonies or compound interest.
What is an exponential function?
This type of discontinuity is the only one we've covered in which a limit may exist.
This theorem states that for a given planar arc between two endpoints, there is at least one point at which the tangent to the arc is parallel to the secant through its endpoints.
What is the mean value theorem (MVT)?
This mathematical term refers to a value that has both direction and magnitude. One real-world example of this is force.
What is a vector?
This is the limit as x approaches 0 of (1 / x^5).
What is D.N.E./ "no limit"?
This function is the result of dividing one polynomial by another, and can produce infinite discontinuity?
What is a rational function?
This type of discontinuity involves real, constant limits from both the left and right sides, but these values do not converge.
What is a jump discontinuity?
This theory is used to find the limit of a function via comparison with two other functions that sandwich the first and whose limits are known and easy to find.
What is the squeeze theorem?
In statistics, this is an averaged measure that is used to quantify the amount of variation or dispersion of a set of data values.
What is standard deviation?
This is the limit as x --> - infinity of the function (0.5^x)
What is infinity?
This function represents the inverse of an exponential function and a clear favorite among beavers.
This type of discontinuity is always accompanied by a vertical asymptote.
What is an infinite discontinuity?
This famous theory states that if a continuous function, f, with an interval, [a, b], as its domain, takes values f(a) and f(b) at each end of the interval, then it also takes any value between f(a) and f(b) at some point within the interval .
What is the Intermediate Value Theorem (IVT)?
Unlike the vast majority, this type of quadrilateral is concave.
What is a chevron?
These are the three conditions for a function's continuity at a point c.
What are: The function is defined at the point. the function has a limit from one or both sides of that point. The limit equals the value of the function at the point.
This function is not a polynomial, yet it still has a vertex.
What is absolute value function?
This type of discontinuity is one that we haven't discussed, but can actually yield a definitive limit using the squeeze theorem.
What is oscillating discontinuity?
This rule helps to find the limit of rational functions who would otherwise be indeterminate by deriving both numerator and denominator.
What is L'Hopital's Rule?
This is the probability that 5 coins tossed in the air will result in 3 heads and 2 tails.
What is 5 / 16?
5C2 / 2^5 or 5C3/2^5