MORE ON VERTICAL TANGENT LINES 1. Introduction In Thomas
... 3. A function for which (1.1) is true but (1.2) is false Sometimes funny things can happen. We are about to define a function f which approaches a vertical line as x approaches x0 = 0, but which is so wobbly on small scales that f 0 (x) actually alternates between positive and negative values rapidl ...
... 3. A function for which (1.1) is true but (1.2) is false Sometimes funny things can happen. We are about to define a function f which approaches a vertical line as x approaches x0 = 0, but which is so wobbly on small scales that f 0 (x) actually alternates between positive and negative values rapidl ...
Recall that, given an infinitely differentiable function f
... This converges for all x by the ratio test. By the k th term test we know that N → 0 as N → ∞. By the above the k th term must go to zero. Thus (x−c) N! N +1 ...
... This converges for all x by the ratio test. By the k th term test we know that N → 0 as N → ∞. By the above the k th term must go to zero. Thus (x−c) N! N +1 ...
Algebra 2 – PreAP/GT
... A student group is selling chocolate bars for $2 each. The function f x 2 x gives the amount of money collected after selling x chocolate bars. f x would be considered a discrete function since only whole number of chocolate bars can be sold which would result in a graph of separated point ...
... A student group is selling chocolate bars for $2 each. The function f x 2 x gives the amount of money collected after selling x chocolate bars. f x would be considered a discrete function since only whole number of chocolate bars can be sold which would result in a graph of separated point ...
Idiosynchromatic Poetry
... Ramsey theory is generally concerned with problems of finding structures with some kind of homogeneity in superstructures. Often a structure contains an homogeneous substructure of a certain sort if it is itself large enough. In some contexts the notion of size can not only be interpreted as cardina ...
... Ramsey theory is generally concerned with problems of finding structures with some kind of homogeneity in superstructures. Often a structure contains an homogeneous substructure of a certain sort if it is itself large enough. In some contexts the notion of size can not only be interpreted as cardina ...
Abel's Version of Abel's Theorem
... I don’t find this simple form of the theorem in the literature (other than in Abel’s memoir itself). The reason, I believe, is that Abel’s setting of the theorem does not fit well with modern ways of thinking. For one thing, the overiding importance of the function concept in modern mathematics obsc ...
... I don’t find this simple form of the theorem in the literature (other than in Abel’s memoir itself). The reason, I believe, is that Abel’s setting of the theorem does not fit well with modern ways of thinking. For one thing, the overiding importance of the function concept in modern mathematics obsc ...
Worksheet - West High School
... Try to find the values of a, b, c, and d by using the Factor Theorem and dividing out each factor as you successfully find it. ...
... Try to find the values of a, b, c, and d by using the Factor Theorem and dividing out each factor as you successfully find it. ...
Fundamental theorem of calculus
The fundamental theorem of calculus is a theorem that links the concept of the derivative of a function with the concept of the function's integral.The first part of the theorem, sometimes called the first fundamental theorem of calculus, is that the definite integration of a function is related to its antiderivative, and can be reversed by differentiation. This part of the theorem is also important because it guarantees the existence of antiderivatives for continuous functions.The second part of the theorem, sometimes called the second fundamental theorem of calculus, is that the definite integral of a function can be computed by using any one of its infinitely-many antiderivatives. This part of the theorem has key practical applications because it markedly simplifies the computation of definite integrals.