Here, you will learn what is the section formula and distance formula and and applications of distance formula. Let’s begin – Section Formula – for internal and external division The co-ordinates of a point dividing a line joining the points P(\(x_1,y_1\)) and Q(\(x_2,y_2\)) in the ratio m : n is given by : (a) for …
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Here, you will learn formulas for definite integrals and properties of definite integrals with examples. Let’s begin – A definite integral is denoted by \(\int_{a}^{b}\) f(x)dx which represent the algebraic area bounded by the curve y = f(x), the ordinates x = a, x = b and the x-axis. Properties and Formulas for Definite Integrals …
Here, you will learn state polygon law of vector addition, subtraction of vectors and multiplication of vector by scalars. Let’s begin – Polygon law of vector Addition (Addition of more than two vectors) Addition of more than two vectors is found to be by repetition of triangle law. Suppose we have to find the sum …
Here, you will learn triangle law of addition of vectors and parallelogram law of addition of vectors and properties of vector addition. Let’s begin – Addition of Vectors The vectors have magnitude as well as direction, therefore their addition is different than addition of real numbers. Let \(\vec{a}\) and \(\vec{b}\) be two vectors in a …
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Here, you will learn vector quantities and scalar quantities and mathematical description of vector and scalar. Let’s begin – Vectors constitute one of the several Mathematical systems which can be usefully employed to provide mathematical handling for certain types of problems in Geometry, Mechanics and other branches of Applied Mathematics. Vectors facilitate mathematical study of …
Here, you will learn what is inverse of a function, its properties and how to find the inverse of a function. Let’s begin – Inverse of a Function Let f : A \(\rightarrow\) B be a one-one & onto function, then there exists a unique function g : B \(\rightarrow\) A such that f(x) = …
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Here, you will learn what is a periodic function with definition and example. Let’s begin – Periodic Function A function f(x) is called periodic if there exist a positive number T (T > 0), where T is the smallest such value called the period of the function such that f(x + T) = f(x), for …
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Here, you will learn one one and onto function (bijection) with definition and examples. Let’s begin – What is Bijection Function (One-One Onto Function) ? Definition : A function f : A \(\rightarrow\) B is a bijection if it is one-one as well as onto. In other words, a function f : A \(\rightarrow\) B …
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Here, you will learn formulas for inverse trigonometric functions, equation and inequations involving inverse trigonometric function. Let’s begin – Simplified Inverse Trigonometric Functions (a) y = f(x) = \(sin^{-1}({2x\over {1+x^2}})\) = \(\begin{cases} 2tan^{-1}x, & \text{if}\ |x| \le 1 \\ \pi – 2tan^{-1}x, & \text{if}\ x > 1 \\ -(\pi + 2tan^{-1}x), & \text{if}\ x < …
Here, you will learn the definition of bayes theorem and the formula for bayes theorem with example. Let’s begin – Formula for Bayes Theorem Let an event A of an experiment occurs with its n mutually exclusive & exhaustive events \(B_1\), , \(B_2\), \(B_3\),………\(B_n\) & the probabilities P(A/\(B_1\)), P(A/\(B_2\))……..P(A/\(B_n\)) are known, then P(\(B_i\)/A) = \(P(B_i).P(A/B_i)\over …
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