
Problems only - Georg Mohr
... 98.1. Determine all functions f defined in the set of rational numbers and taking their values in the same set such that the equation f (x + y) + f (x − y) = 2f (x) + 2f (y) holds for all rational numbers x and y. 98.2. Let C1 and C2 be two circles intersecting at A and B. Let S and T be the centres ...
... 98.1. Determine all functions f defined in the set of rational numbers and taking their values in the same set such that the equation f (x + y) + f (x − y) = 2f (x) + 2f (y) holds for all rational numbers x and y. 98.2. Let C1 and C2 be two circles intersecting at A and B. Let S and T be the centres ...
Chapter I
... The Algebraic and Order Properties of R: Algebraic Properties of R: A1. a +b = b +a a, b R . A2. (a +b) +c = a +(b +c) a, b, c R . A3. a +0 = 0 +a = a a R . A4. a R there is an element a R such that a +(-a ) = (-a ) +a = 0. M1. a .b = b .a a, b R . M2. (a .b) .c = a .(b .c) a, b, c ...
... The Algebraic and Order Properties of R: Algebraic Properties of R: A1. a +b = b +a a, b R . A2. (a +b) +c = a +(b +c) a, b, c R . A3. a +0 = 0 +a = a a R . A4. a R there is an element a R such that a +(-a ) = (-a ) +a = 0. M1. a .b = b .a a, b R . M2. (a .b) .c = a .(b .c) a, b, c ...
Generating Prime Numbers
... one composite image. In [1] they improve the result by proving the following theorem. Theorem 2. Given a positive integer n, f (x) takes an infinite number of values that are divisible by at least n distinct primes, and an infinite number of values that are divisible by pn for some prime p. In [4] t ...
... one composite image. In [1] they improve the result by proving the following theorem. Theorem 2. Given a positive integer n, f (x) takes an infinite number of values that are divisible by at least n distinct primes, and an infinite number of values that are divisible by pn for some prime p. In [4] t ...
Intermediate Value Theorem and Maple
... can also keep applying the IVT by evaluating the function f at the following numbers starting at 1.220740 and increasing the digit in the millionths place by one until we reach 1.220750. We will see that our solution (root) is somewhere between these two numbers. We want to identify the first place ...
... can also keep applying the IVT by evaluating the function f at the following numbers starting at 1.220740 and increasing the digit in the millionths place by one until we reach 1.220750. We will see that our solution (root) is somewhere between these two numbers. We want to identify the first place ...
Calc 2.2 - Hill City SD 51-2
... Finite limits as x→±∞ The symbol for infinity (∞) does not represent a real number. We use ∞ to describe the behavior of a function when the values in its domain or range outgrow all finite bounds. For example, when we say “the limit of f as x approaches infinity” we mean the limit of f as x moves ...
... Finite limits as x→±∞ The symbol for infinity (∞) does not represent a real number. We use ∞ to describe the behavior of a function when the values in its domain or range outgrow all finite bounds. For example, when we say “the limit of f as x approaches infinity” we mean the limit of f as x moves ...