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Articles by Praveen Varghese Thomas
Page 17 of 75
Second Order Derivative
Introduction In calculus, Derivatives are a basic tool in solving problems and differential equations. Derivatives are used as a tool by scientists to analyse dynamic systems to determine the change in variables, and use this to frame differential equations, and use integration to predict the future changes. To put simply, a second-order derivative is the two consequent derivatives of a function, or it is the derivative of the first order derivative of that function. In this tutorial, we will learn about derivatives, order of derivatives, second order derivatives, second order derivatives of parametric functions, and some solved examples. Derivative Derivative ...
Read MoreSection Formula in 3D
Introduction The section formula can be applied to a line segment located in 2D or 3D. The division of a line segment is a method or process in which the line segment is divided into several parts (equal or non-equal). Points are used to divide a line segment. It is an important method used in coordinate geometry to determine the centroid, incenter, and excenter of a triangle. In this tutorial, we will discuss the 3D geometry, section formula, and distance formula with solved examples. 3D Coordinate Geometry The 3D coordinate geometry represents the geometrical figures in 3D space. It requires ...
Read MoreRelations and Functions
Introduction A relation is defined as the mutual dependence of one element on another. In mathematics, the function represents the specific relationships between two sets of elements. In this tutorial, we will discuss the meaning of relations and functions, their various types, and the inverse of a function with solved examples. Relations The relation is a binary relation between two classes or sets, representing that the elements of both classes are somehow related. The binary relation between two sets X and Y is a set of ordered pairs of elements, i.e., (x, y), in such a way that the element ...
Read MoreRight angled triangle: Constructions (RHS)
Introduction The word trigonometry means tri-angle-measurements which is three angle measurement. When we take any polygon, such as square, rectangle, pentagon, hexagon, etc., we can divide each polygon into triangles. So trigonometry mainly deals with triangles. There are three types of triangle based on the angle measurements. They are acute angled triangle, obtuse angled triangle, right angle triangle. Acute angled triangle − All the three interior angles measured are less than 90°. Obtuse angled triangle − All the three interior angles measured are greater than 90°. Right angled triangle − At Least one of the interior angles measures 90°. Right ...
Read MoreRight Circular Cylinder
Introduction A three-dimensional solid figure is called the right circular cylinder. There is a closed circular surface on both ends of the right circular cylinder, which are parallel to one another. The right cylinder is another name for a right circular cylinder. All of the points on the closed surface are equally spaced from the axis of the right circular cylinder. In everyday life, a right circular cylinder is the most typical 3D figure. The correct round cylinder can be created by stacking many circular pieces of paper. It is known as a right circular cylinder because it has been ...
Read MoreRolle’s Theorem and Lagrange’s Mean Value Theorem
Introduction Rolle’s theorem and Lagrange’s mean value theorem are interpreted on a function over an interval if the function satisfies the condition of continuity over a given closed interval and the condition of differentiability over a given open interval. The continuity of a function over a closed interval is defined as the function's graph that should not contain any break over the interval. The differentiability of a function over an open interval is defined as the function should be differentiable at every point in the interval. Continuity and Differentiability Continuity: Let’s take a function 𝑓(𝑥) with a domain and ...
Read MoreRoman Numerals Conversion
Introduction In the Middle Ages, the roman number system is considered a standard writing system for numbers throughout Europe. Romans invented it for daily life because they could not count more than ten using their fingers. Latin numbers are the words in Latin that are used to count numbers. They are also represented by roman numerals but are read in Latin. Roman numbers consist of symbols containing alphabets as some base numbers. Numbers Numbers play a huge part in daily life and mathematics. They are used to counting things, without numbers it is tough to count and remember the ...
Read MoreRoots of Polynomials
Introduction A wide group of algebraic expressions are combined to form the Polynomials. They can have constants, variables and exponents or, say, powers. The powers of the variables are positive whole numbers and not any fractions when we consider any expressions of the polynomials. Polynomials don't have any square root of variables or the negative powers on the variables. The coefficient of a polynomial is the number multiplied by a variable. The number which does not involve any variable or say, the number multiplied by the variable with power zero is called the constant of the polynomial. The degree of ...
Read MoreQuadratic Formula
Introduction The quadratic equation is a one-variable polynomial equation with degree two. The highest power of the unknown variable in a quadratic equation is two. The general form of a quadratic equation f(x) with variable x is f(x)=ax2+bx+c=0, in which a≠0 and a, b, c ϵ R. Every quadratic equation has two roots which can be real or imaginary. The discriminant of a quadratic equation determines the nature of the roots. The roots can be calculated using the quadratic formula. Quadratic Equations A Quadratic equation is a polynomial equation of one variable with a degree of two. The general ...
Read MoreRelation Between Coefficients and Zeros of a Polynomial
Introduction Polynomials are mathematical expressions containing variables and coefficients. James Waddell Alexander II invented the concept of the polynomial. There are various terms associated with the polynomial. In this tutorial, we will discuss the meaning of polynomial, various correlations between the zeroes and the coefficients of polynomial equations with solved examples. Polynomials Polynomials are defined as the algebraic expressions containing one or more variable terms multiplied by constant terms. There are two terms associated with a polynomial, such as coefficients (i.e., constants) and variables. For example, $\mathrm{\mathit{f}(p)=p^2+2p+5}$ is an example of a polynomial. The given polynomial is denoted by f(p). ...
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