A.5 - DPS ARE
... Expressions – A-APR ELG.MA.HS.A.5: Use polynomial identities to solve problems. A-APR.C.5 (+) Know and apply the Binomial Theorem for the expansion of (x + y)n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle. ...
... Expressions – A-APR ELG.MA.HS.A.5: Use polynomial identities to solve problems. A-APR.C.5 (+) Know and apply the Binomial Theorem for the expansion of (x + y)n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle. ...
A new proof of the maximal monotonicity of
... We give a new proof based on the recent very elegant argument of Marques Alves and Svaiter that the subdifferential of a proper, convex lower semicontinuous function on a real Banach space is maximally monotone. We also show how the argument can be simplified in the reflexive case. Basic notation an ...
... We give a new proof based on the recent very elegant argument of Marques Alves and Svaiter that the subdifferential of a proper, convex lower semicontinuous function on a real Banach space is maximally monotone. We also show how the argument can be simplified in the reflexive case. Basic notation an ...
MAXIMA AND MINIMA
... The fundamental theorem of algebra states that in the field of complex numbers every polynomial equation has at least one root. As a consequence of this theorem, it can be proved that every nth degree polynomial has n roots in the complex field. When complex numbers are admitted, the polynomial theore ...
... The fundamental theorem of algebra states that in the field of complex numbers every polynomial equation has at least one root. As a consequence of this theorem, it can be proved that every nth degree polynomial has n roots in the complex field. When complex numbers are admitted, the polynomial theore ...
Analysis Aug 2010
... norm to f . You may as well assume that gN is a linear combination of 1 , 2 , . . . MN , where M1 < M2 < M3 < . . .. (Why can you assume this?) Now consider the subsequence ||f SMN (f )|| of ||f SN (f )||. (d) True or false: under the hypotheses of part (c) above, S is, in fact, an orthonormal basis ...
... norm to f . You may as well assume that gN is a linear combination of 1 , 2 , . . . MN , where M1 < M2 < M3 < . . .. (Why can you assume this?) Now consider the subsequence ||f SMN (f )|| of ||f SN (f )||. (d) True or false: under the hypotheses of part (c) above, S is, in fact, an orthonormal basis ...
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.