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Dependent and Independent Events in Probability

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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What is Squeeze Theorem – Limit of Exponential Functions

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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How to Find Limit of Trigonometric Functions

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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How to Solve Indeterminate Forms of Limits

Here, you will learn how to solve indeterminate forms of limits and general methods to be used to evaluate limits with examples. Let’s begin –  Indeterminate Forms of Limits \(0\over 0\), \(\infty \over \infty\), \(\infty – \infty\),\(0\times \infty\), \(1^{\infty}\), \(0^0\), \({\infty}^0\) Note : (i)  Here 0, 1 are not exact, infact both are approaching to …

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Trigonometric Equations Solving Strategies

Here, you will learn trigonometric equations solving strategies i.e by factorisation and reducing it to a quadratic equation etc. Let’s begin – Different Strategies for Trigonometric Equations Solving (a) Solving trigonometric equations by factorisation Example : If \(1\over 6\)sin x, cos x, tan x are in G.P. then the general solution for x is Solution …

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What is Vector Triple Product

Here, you will learn what is vector triple product formula and linear independence and dependence of vectors. Let’s begin – Vector Triple Product Formula Let \(\vec{a}\), \(\vec{b}\) and \(\vec{c}\) be any three vectors, then the expression \(\vec{a}\times (\vec{b}\times\vec{c})\) is a vector & is called a vector triple product. Linear Independence And Dependence of Vectors (a)  …

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