Power series with Complex Coefficient. n represents the coefficient of the nth term and c is a constant. An is independent of x and may be expressed as a function of n . The set of all formal power series in X with coefficients in a commutative ring R form another ring that is written R [[ X ]] Also expressions for Coefficients of a Power Series. As […]
Power series with Real Coefficient
Power series with Real Coefficients. The exponential function (in blue), and the sum of the first n + 1 terms… Radius of convergence. A power series will converge for some values of the variable x… Operations on power series. Power Series
Rules of Transformation
In this post question are from transformations of function. It basically deals with translation of functions through vector . Also it deal with reflection. Transformation
Volume of Solids of revolution
Volume of solid of revolutions of a function, y=f (x), on an interval [a,b]. When we rotate this curve about a given axis we get the surface of the solid of revolution. Similarly Disk method. If the axis of revolution is the boundary of the plane region and perpendicular to the axis of revolution. Therefore Solid of revolution. A […]
Circles and sectors
Circles, Arcs and Sectors of Circle. A circle has three main components: The circumference, which is the outside edge of the circle. The radius, which goes from any point on the circumference to the centre of the circle. Circle and Sector
Fundamentals of Counting Principal , Per...
The Fundamental Counting Principle and Permutations is a way to figure out the total number of ways different events can occur. In combinatorics, the rule of product or multiplication principle is a basic counting it is the idea . Hence this principle also used in permutation and combination. Counting Principles
Derivative test
First Derivative Test for Local Extrema. If the derivative changes from positive (increasing function) to negative (decreasing function), the function has a local (relative) maximum at the critical point. Second Derivative Test. 1. If , then has a local minimum at . 2. If , then has a local maximum at . The extremum test gives slightly more general conditions under which […]
Volume of 3d Shapes and Sides of Polygon...
3D Shapes and Volume. 3D shapes have volume: the amount of cubic space inside of them. To find volume, you basically need the three dimensions: length, width, and height. For prisms, the formulas are derived by taking the area of the shape at the end, and multiplying that times the figure’s height. All regular polygons have at least one axial symmetry. A regular polygon with as many axes of symmetry as it possesses sides. The axes of […]
Unit Circle
Unit circle is base for trigonometric table . This table consist of ratio, values and angles. It also use for establishing pythagorean identity. Further these identity use in simplification of equations. Hence equation to be solve. Unit Circle
Trigonometric Plane
Trigonometric plane for sign convention of trigonometric ratio in quadrants. There are four quadrants in plane and six trigo ratio. This is useful while finding angle for given value. Also we required for sketching trigo graph. As curve both side of x-axis. Trigonometric Plane
