![[2013 question paper]](http://s1.studyres.com/store/data/008844914_1-fdd71aa622fa0ea68704ae0c1d1e6636-300x300.png)
[2013 question paper]
... 1. Let f (x) = x cos x for x ∈ R. Then (A) there is a sequence xn → −∞ such that f (xn ) → 0. (B) There is a sequence xn → ∞ such that f (xn ) → ∞. (C) there is a sequence xn → ∞ such that f (xn ) → −∞. (D) f is a uniformly continuous function. 2. The equation x10 + a9 x9 + a8 x8 + · · · + a1 x − 5 ...
... 1. Let f (x) = x cos x for x ∈ R. Then (A) there is a sequence xn → −∞ such that f (xn ) → 0. (B) There is a sequence xn → ∞ such that f (xn ) → ∞. (C) there is a sequence xn → ∞ such that f (xn ) → −∞. (D) f is a uniformly continuous function. 2. The equation x10 + a9 x9 + a8 x8 + · · · + a1 x − 5 ...
Algebraic Numbers - Département de Mathématiques d`Orsay
... of the shape qX + qY − p (with nonzero integers p and q) satisfies P (e, π) = 0. A stronger conjecture is the following: Conjecture 2.1 The numbers e and π are algebraically independent. However, the same question with π and eπ has been answered: Theorem 2.2 (Nesterenko, 1996) The numbers π and eπ a ...
... of the shape qX + qY − p (with nonzero integers p and q) satisfies P (e, π) = 0. A stronger conjecture is the following: Conjecture 2.1 The numbers e and π are algebraically independent. However, the same question with π and eπ has been answered: Theorem 2.2 (Nesterenko, 1996) The numbers π and eπ a ...
Pythagoras Solution
... 24. Four friends W, X, Y, and Z are walking in a straight line. Y is not second. X is right behind Y. Z is right behind W, who is not third. Taking into account all of these constraints, we can draw the diagram below. We can see in this diagram, that only Y or Z can be third. Z cannot be third becau ...
... 24. Four friends W, X, Y, and Z are walking in a straight line. Y is not second. X is right behind Y. Z is right behind W, who is not third. Taking into account all of these constraints, we can draw the diagram below. We can see in this diagram, that only Y or Z can be third. Z cannot be third becau ...
Math 475 Big Problems, Batch 2 Big Problem 7: Tulie Number
... Big Problem 7: Tulie Number Flipping. Tulie has just discovered the Reciprocal button on her calculator (it’s labeled “x−1 ”on the TI-83+). First she noticed that if you enter a number and take the reciprocal, and then take the reciprocal of the result, you get back the original number. This was a l ...
... Big Problem 7: Tulie Number Flipping. Tulie has just discovered the Reciprocal button on her calculator (it’s labeled “x−1 ”on the TI-83+). First she noticed that if you enter a number and take the reciprocal, and then take the reciprocal of the result, you get back the original number. This was a l ...
A.34
... - Perfect Squares and Perfect Cubes (evaluating them to a single number) - Expressing other powers of a number using exponents - Factoring a number (if you cannot factor, then the number is prime) - Finding the Greatest Common Factor of two numbers Please review ALL notes and HW assignments in addit ...
... - Perfect Squares and Perfect Cubes (evaluating them to a single number) - Expressing other powers of a number using exponents - Factoring a number (if you cannot factor, then the number is prime) - Finding the Greatest Common Factor of two numbers Please review ALL notes and HW assignments in addit ...
Full text
... that x + y is a prime greater than p . If x 4- y is composite, it must have a prime divisor greater than p. . This last statement follows from the fact that every prime q<.Vk divides m and hence divides x. If q divides x + y, then it divides y9 which contradicts the fact that (x9 y, 2) is a primitiv ...
... that x + y is a prime greater than p . If x 4- y is composite, it must have a prime divisor greater than p. . This last statement follows from the fact that every prime q<.Vk divides m and hence divides x. If q divides x + y, then it divides y9 which contradicts the fact that (x9 y, 2) is a primitiv ...
Lesson 1 - Integers and the Number Line
... The ‘ …’ means that that number pattern goes on forever ( to infinity) … Ex: 1, 2, 3, 4, 5… Whole numbers: natural numbers AND zero Ex: 0, 1,2,3 Integers: positive and negative whole numbers (what you see on a number line). - Are negative and positive whole numbers (they don’t have decimals and are ...
... The ‘ …’ means that that number pattern goes on forever ( to infinity) … Ex: 1, 2, 3, 4, 5… Whole numbers: natural numbers AND zero Ex: 0, 1,2,3 Integers: positive and negative whole numbers (what you see on a number line). - Are negative and positive whole numbers (they don’t have decimals and are ...