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 […]
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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 <
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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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Here, you will learn formula for binomial probability distribution in probability with example. Let’s begin – Suppose that we have an experiment such as tossing a coin or die repeatedly or choosing a marble from an urn repeatedly. Each toss or selection is called a trial. In any single trial there will be a probability
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Here, you will learn dependent and independent events in probability with examples. Let’s begin – Dependent and Independent Events Formula Two Events A and B are said to be independent if occurrence or non-occurrence of one does not affect the probability of the occurrence or non-occurrence of other. If the occurrence of one event affects
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Here, you will learn what is squeeze theorem or sandwich theorem of limit and limit of exponential function with examples. Let’s begin – Squeeze Theorem (Sandwich Theorem) If f(x) \(\leq\) g(x) \(\leq\) h(x); \(\forall\) x in the neighbourhood at x = a and \(\displaystyle{\lim_{x \to a}}\) f(x) = l = \(\displaystyle{\lim_{x \to 1}}\) h(x) then
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Here, you will learn how to find limit of trigonometric functions and limits using series expansion with example. Let’s begin – Limit of Trigonometric Functions \(\displaystyle{\lim_{x \to 0}}\) \(sinx\over x\) = 1 = \(\displaystyle{\lim_{x \to 0}}\) \(tanx\over x\) = \(\displaystyle{\lim_{x \to 0}}\) \(tan^{-1}x\over x\) = \(\displaystyle{\lim_{x \to 0}}\) \(sin^{-1}x\over x\) [where x is measured in
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