A fork of Rural Dictionary
An expression such as x^3 + 2x^2 - 6x - 2, is a cubic expression. 3x - 4 is linear x^2 + 5x - 10 is quadratic These types of expressions can be extended to include higher powers of x, such as x^5 + 3x^3 - 2x^2 + 3 4x^6 + 2x^4 - x^3 + 5 Expressions of this type are called polynomials. Note: Polynomials do not have negative or fractional powers. n is a non-negative integer. The degree of a polynomial is given by the highest power of the variable
An expression of the form ax^n + bx^(n-1) + ... + px^2 + qx + r (where a, b, ..., p, q, r are constants is called a polynomial in x) 3x^5 + 3x^4 - 2x^2 -1 is a polynomial of degree 5. A constant expression is a polynomial of degree 0 A linear expression is a polynomial of degree 1 a quadratic expression is a polynomial of degree 2 a cubic expression is a polynomial of degree 3 etc.
In mathematics, we often arrive at answers that contain root signs (they may be square roots, cube roots, etc.). We will find that some of these numbers with a root sign are easy to deal with since they have an exact decimal representation For instance sqrt16 = 4, rt^3(8)= = 2, sqrt11.56 = 3.4, rt^5(1/32) = 0.5. This is because each of these numbers is rational
Expressions with root signs involving pirrational numbers such as sqrt7 - 2 or rt^3(5) are called surds.
the reverse process of differentiaton we know that, for example if f(x) = 2x^3 - 5x^2 + 3x -7 then f'(x) = 6x^2 - 10x + 3 This process can be reversed. In general, y = x^n -> dy/dx = nx^(n-1) So, reversing this process, it would seem that dy/dx = x^m -> y = (1/(m+1))x^(m+1) The general process of finding a function from its derivative is known as interation.
Given that dy/dx = 12x^2 + 4x - 5, find an expression for y. y = 12((x^3)/3) + 4((x^2)/2) - 5((x^1)/1) It would seem that y=4x^3 + 2x^2 - 5x but that is not quite the complete answer Whenever you differentiate a constant you get zero, e.g. y = 7 dy/dx = 0 and so the expression for y above could have any constant on the end and still satisfy dy/dx = 12x^2 + 4x - 5 The answer to this example is therefore y= 4x^3 + 2x^2 - 5x + c, where c is a constant.
The plural of index is indices Index is simply another word for power.
a * a * a * a can be written as a^4 (a to the power of 4)