Math 112 Lecture 1: Introduction to Limits
... Two Sided Nature of Limits We must be able to make f (x ) arbitrarily close to L by making x sufficiently close to a, on either side of a. In some cases we get a different value if we make x close to a on different sides of a. In this case the limit does not exist. This leads to the idea of one-side ...
... Two Sided Nature of Limits We must be able to make f (x ) arbitrarily close to L by making x sufficiently close to a, on either side of a. In some cases we get a different value if we make x close to a on different sides of a. In this case the limit does not exist. This leads to the idea of one-side ...
![1. Positive implicational Hilbert`s logic H→ (see [9], ch.3)](http://s1.studyres.com/store/data/002031595_1-a8999ab099c38ccf3594f4ea3d7df0e8-300x300.png)
The Riemann hypothesis
... We have proved that the non trivial zeros of the Riemann function for the reals lie in the critical line ! So the hypothesis is proved for the real numbers. The Riemann hypothesis is important because it gives information about the zeros of the Riemann function and the distribution of those zeros ar ...
... We have proved that the non trivial zeros of the Riemann function for the reals lie in the critical line ! So the hypothesis is proved for the real numbers. The Riemann hypothesis is important because it gives information about the zeros of the Riemann function and the distribution of those zeros ar ...
SMOOTH CONVEX BODIES WITH PROPORTIONAL PROJECTION
... A convex body in Rn is a compact convex set with nonempty interior. If K is a convex body and L a linear subspace of Rn , then K|L is the orthogonal projection of K onto L. Let G(n, i) be the Grassmannian of all i-dimensional linear subspaces of Rn . A central question in the geometric tomography of ...
... A convex body in Rn is a compact convex set with nonempty interior. If K is a convex body and L a linear subspace of Rn , then K|L is the orthogonal projection of K onto L. Let G(n, i) be the Grassmannian of all i-dimensional linear subspaces of Rn . A central question in the geometric tomography of ...
Contents - CSI Math Department
... For the impatient: A function in mathematics is defined as ”a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.” That is a general definition. Specialized to mathematical functions of one real variable returning a re ...
... For the impatient: A function in mathematics is defined as ”a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.” That is a general definition. Specialized to mathematical functions of one real variable returning a re ...
Some Polynomial Theorems
... Since $%&' only had degree 2 in the first place, +2 %&' must be of degree 0 making +2 %&' some constant, say +2 %&' - 53 Now ;2/1 is still a zero of $%&'@ and since ;2/1 is distinct from all the other ;C @ we must have +2 %;2/1 ' - *3 The only way this can happen is if 5 - * and this would imply $%& ...
... Since $%&' only had degree 2 in the first place, +2 %&' must be of degree 0 making +2 %&' some constant, say +2 %&' - 53 Now ;2/1 is still a zero of $%&'@ and since ;2/1 is distinct from all the other ;C @ we must have +2 %;2/1 ' - *3 The only way this can happen is if 5 - * and this would imply $%& ...
Infinite Sequences
... Another way to understand this is that if lim an = L then jan Lj goes to 0 n!1 when n ! 1. It should also be noted that if lim an = L, then lim an+1 = L. n!1 n!1 In fact, lim an+p = L for any positive integer p. Graphically, the meaning of lim an = L is as follows. Consider the sequence shown on …gu ...
... Another way to understand this is that if lim an = L then jan Lj goes to 0 n!1 when n ! 1. It should also be noted that if lim an = L, then lim an+1 = L. n!1 n!1 In fact, lim an+p = L for any positive integer p. Graphically, the meaning of lim an = L is as follows. Consider the sequence shown on …gu ...
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.