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MATH 115, SUMMER 2012 LECTURE 5 Last time:
MATH 115, SUMMER 2012 LECTURE 5 Last time:

... The following two theorems are very useful; the second follows from the first. To motivate these two results, recall an important caution: you cannot substitute congruent numbers as exponents! For example, even though 1 ≡ 5 mod 4, it is not true that 21 ≡ 25 mod 4. So when can we use congruence to s ...
(pdf)
(pdf)

(1,1)fyy - KSU Web Home
(1,1)fyy - KSU Web Home

Densities and derivatives - Department of Statistics, Yale
Densities and derivatives - Department of Statistics, Yale

... For example, if µ is Lebesgue measure on B(R), the probability measure defined by the density (x) = (2π )−1/2 exp(−x 2 /2) with respect to µ is called the standard normal distribution, usually denoted by N (0, 1). If µ is counting measure on N0 (that is, mass 1 at each nonnegative integer), the pro ...
fermat`s little theorem - University of Arizona Math
fermat`s little theorem - University of Arizona Math

Transcript - Lecture 3: Three-Dimensional Area
Transcript - Lecture 3: Three-Dimensional Area

36(2)
36(2)

Continuity and one
Continuity and one

... has a jump discontinuity at x=-2 b) To decide the continuity in its entirety, it is needed to check each function´s continuity. The first function, f ( x)  2x  1 for x   , 2 is continuous in its entirety of domain, the second function f ( x)  1  x2 for x   2, 2 also is continuous in it ...
Lesson 7.3 - Coweta County Schools
Lesson 7.3 - Coweta County Schools

Numeration 2016 - Katedra matematiky
Numeration 2016 - Katedra matematiky

... The combination of this fact with a useful result of B. Kovács – A. Pethő [11] on certain constants associated to an algebraic integer allows a modification of the above mentioned algorithm for the computation of CNS bases. Theorem 2 (B. – Huszti – Pethő [8]). Let γ be an algebraic integer and Cγ be ...
39(3)
39(3)

An Example of Induction: Fibonacci Numbers
An Example of Induction: Fibonacci Numbers

Sheffer sequences, probability distributions and approximation
Sheffer sequences, probability distributions and approximation

19(2)
19(2)

Real Zeros of Polynomial Functions - peacock
Real Zeros of Polynomial Functions - peacock

... number that is equal to f(a). 1. i.e.. If f(x) is divided by x – 4, f(4) will give the value of the remainder. Dividend = (quotient ∙ divisor) + remainder 1. Also can see this as f(x) = [q(x) ∙ (x – a)] + f(a). 2. The quotient is always a polynomial with one degree less than f(x). ...
Logic and Mathematical Reasoning
Logic and Mathematical Reasoning

x - Montgomery County Schools
x - Montgomery County Schools

... Continuity Continuity at a Point The basic idea is as follows: We are given a function f and a number c. We calculate (if we can) both lim f  x  and f (c). If these two numbers are equal, we x c say that f is continuous at c. Here is the definition formally stated. ...
An Example of Induction: Fibonacci Numbers
An Example of Induction: Fibonacci Numbers

SECTION 2.5: FINDING ZEROS OF POLYNOMIAL FUNCTIONS
SECTION 2.5: FINDING ZEROS OF POLYNOMIAL FUNCTIONS

Number Theory II: Congruences
Number Theory II: Congruences

Section 4.1: The Definite Integral
Section 4.1: The Definite Integral

1 8.5 Trigonometric Substitution –– Another Change of
1 8.5 Trigonometric Substitution –– Another Change of

6.3 Derangements Suppose each person in a group of n friends
6.3 Derangements Suppose each person in a group of n friends

... that n − 1 is in the nth position. We need to partition the permutations in Rn−1 into two sets, one with Dn−2 elements and the other with Dn−1 elements. We can easily take care of Dn−2 . The numbers n − 1 and n do not appear in any derangement of {1, ..., n − 2}. In Rn−1 , n − 1 appears in the last ...
Partitions
Partitions

Using Mapping Diagrams to Understand Functions
Using Mapping Diagrams to Understand Functions

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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.
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