Permutations and Combinations Student Notes
... 2. Permutations and Factorial Notation Assignment: Workbook pg. 382-384 #1-13, pg. 526 of text #22 3. Permutations with Repetitions and Restrictions Assignment: Workbook: pg. 388 – 391 #1-15, pg. 525 of text #8 4. Combinations – pg. 528-536 Assignment: Workbook: pg. 396 –398 #1-12, pg. 402-404 #1-16 ...
... 2. Permutations and Factorial Notation Assignment: Workbook pg. 382-384 #1-13, pg. 526 of text #22 3. Permutations with Repetitions and Restrictions Assignment: Workbook: pg. 388 – 391 #1-15, pg. 525 of text #8 4. Combinations – pg. 528-536 Assignment: Workbook: pg. 396 –398 #1-12, pg. 402-404 #1-16 ...
Notes on Calculus II Integral Calculus Miguel A. Lerma
... small amounts f (x) dx. The symbol dx was interpreted as the length of an “infinitesimal” interval, sort of what ∆x becomes for infinite n. This interpretation was later abandoned due to the difficulty of reasoning with infinitesimals, but we keep the notation. Remark : Note that in intervals where ...
... small amounts f (x) dx. The symbol dx was interpreted as the length of an “infinitesimal” interval, sort of what ∆x becomes for infinite n. This interpretation was later abandoned due to the difficulty of reasoning with infinitesimals, but we keep the notation. Remark : Note that in intervals where ...
Short effective intervals containing primes
... statement has been proved for almost all intervals in a quadratic average sense by Selberg [19] in 1943 assuming the Riemann hypothesis and replacing K by a function KðxÞ tending arbitrarily slowly to infinity. From a numerical point of view, the Riemann hypothesis is known to hold up to a very large ...
... statement has been proved for almost all intervals in a quadratic average sense by Selberg [19] in 1943 assuming the Riemann hypothesis and replacing K by a function KðxÞ tending arbitrarily slowly to infinity. From a numerical point of view, the Riemann hypothesis is known to hold up to a very large ...
Sets and functions
... 1. For any set X, the identity function Id : X → X satisfies: IdX (x) = x for every x ∈ X. Thus its graph in X 2 is the set {(x, x) : x ∈ X}, which we can think of as the “diagonal” viewed as a subset of X 2 . (Does the diagonal satisfy the test of being the graph of a function?) The preimage of A ...
... 1. For any set X, the identity function Id : X → X satisfies: IdX (x) = x for every x ∈ X. Thus its graph in X 2 is the set {(x, x) : x ∈ X}, which we can think of as the “diagonal” viewed as a subset of X 2 . (Does the diagonal satisfy the test of being the graph of a function?) The preimage of A ...
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.