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Showing posts with label from. Show all posts
Wednesday, March 18, 2015
DEFINITIONS FROM REAL NUMBERS AND POLYNOMIALS STANDARD X
DEFINITIONS FROM REAL NUMBERS
Real Numbers - The collection consisting of all rational and irrational numbers.
Euclids Division Lemma or Euclids Division Algorithm - For any two integers a and b there exist unique whole numbers q and r such that a = bq + r, where 0 is equal to or less than r < b.
Natural Numbers - Counting numbers such as 1,2,3,4......etc. are known as natural numbers.(excluding zero.)
Whole Numbers - All counting numbers together with 0 form the collection of whole numbers.
Integers - All counting numbers along with their negatives and zero form the collection of all integers.
Rational Numbers In Decimal Form - Every Rational Number when expressed in decimal form is expressed either in terminating or in non-terminating repeating decimal form.
Irrational Numbers - The numbers which when expressed in decimal form are expressible as
non-terminating and non-repeating decimals.
DEFINITIONS FROM POLYNOMIALS
Polynomials - An expression of the form p(x) = a(subscript 0) + a(subscript 1)x^1 + a(subscript 2)x^2 + a(subscript 3)x^3 + a (subscript 4)x^4......+a(subscript n)x^n is a polynomial in x of degree n.Here, a(subscript 0),a(subscript 1),a(subscript 2),a(subscript 3),a (subscript 4) are real numbers and each power of x is a non-negative integer.
Linear Polynomials - Polynomials of degree 1 are called Linear Polynomials.The standard form of a linear polynomial is p(x) = ax + b,where a is unequal to zero.
Quadratic Polynomials - Polynomials of degree 2 are called Quadratic Polynomials.The standard form of a quadratic polynomial is p(x) = ax^2 + bx +c,where a is unequal to zero.
Cubic Polynomials - Polynomials of degree 3 are called Cubic Polynomials.The standard forms of a cubic polynomial is p(x) = ax^3 + bx^2 +cx +d,where a is unequal to zero.
Biquadratic Polynomial - Polynomials of degree 4 are called Biquadratic Polynomials.The standard form of a biquadratic polynomial is p(x) = ax^4 + bx^3 +cx^2 +dx+e,where a is unequal to zero.
Value of a Polynomial At a Given Point - If p(x) is a polynomial and α is a real number,then the value obtained by putting x = α in p(x) is called the value of p(x) at x = α.
Zero Of A Polynomial - A real number α is called the zero of the polynomial p(x),if p(α) = 0.
Zero Polynomial - The constant polynomial P(x)=0 whose coefficients are all equal to 0.(Credit : www.mathworld.wolfram.com)
Division Algorithm For Polynomials - If f(x) and g(x) are any two polynomials with g(x) is unequal to zero,then we can find polynomials q(x) and r(x) such that f(x) = q(x)g(x) + r(x) where r(x) = 0 or {degree of r(x)} < {degree of g(x)}.
Credits : Secondary School Mathematics Class X Book,Bharati Bhawan (P & D) by R.S Aggarwal and V Aggarwal,unless any other credit is mentioned along with the definition.
Tuesday, March 17, 2015
Three Outstanding Picture Books from 2014
2014 was a stellar year for picture books. Here are three that I particularly like.
Monday, March 9, 2015
Awesome Creation and Destruction Borne from the Barrel of a Gun
Photos of bullets captured bursting through fragile, everyday objects emanate a rare power. The contrast between lethal, high velocity projectile and prone target hits you, excuse the expression, like a shot. When the object penetrated on impact is as patently childlike as a chocolate bunny, the capacity of the image to make the observer think is amplified – like a gunshot heard for the first time, the weapon’s silencer removed.
This next object is almost unrecognisable – it has been so smashed to smithereens. It’s an egg; an egg with all its associations of innocence and nascent life, utterly obliterated. Impossible not to think of the head of a human or animal upon looking at this exploded household item, to see the viscous remains of shell, yolk and white, frozen mid air, as the inner substance of brain and cranium.
Is this all too serious? Maybe. The photos – like this one of a banana disintegrating – are beautiful after all. And yet what were bullets designed for if not to kill? In an age where gun culture is rife, an age where 29,569 people were killed by guns in the US in 2004 alone, it is impossible to ignore the impact the modern bullet and the gun from which it sprang have had on the world.
A pack of cards; more robust than the other items shot here and yet effortlessly blown apart by a missile less than a centimetre in diameter – as the exit hole and flakes of paper vividly show. Gun politics is a subject as explosive as the weapon in question, with people lining up on both sides to dispute their right to bear arms versus tighter gun control laws. Wherever you stand on this issue, there’s no denying the destructive force of a speeding bullet.Tags:
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