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Differentiation of Constant – Proof and Examples

Here you will learn the differentiation of constant function proof and examples. Let’s begin – Differentiation of Constant The differentiation of constant function is zero. i.e. \(d\over dx\)(c) = 0. Proof : Let f(x) = c, be a constant function. Then, By using first principle, \(d\over dx\) (f(x)) = \(\displaystyle{\lim_{h \to 0}}\) \(f(x + h) …

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Limits at Infinity – Definition and Examples

Here you will learn how to solve or evaluate limits at infinity with examples. Let’s begin – Limits at Infinity Algorithm to evaluate limits at infinity : 1). Write down the given expression in the form of a rational function i.e. \(f(x)\over g(x)\), if it is not so. 2). If k is the highest power …

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Rationalisation Method to Solve Limits

Here you will learn what is the rationalisation method to solve or find limits with examples. Let’s begin – Rationalisation Method to Solve Limits This method is particularly used when either the numerator or denominator or both involve expression consisting of square roots and substituting the value of x the rational expression takes the form …

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Factorisation Method to Solve Limits

Here you will learn what is the factorisation method to solve limits with examples. Let’s begin – Factorisation Method to Solve Limits Consider the following limit : \(\displaystyle{\lim_{x \to a}}\) \(f(x)\over g(x)\) If by substituting x = a, \(f(x)\over g(x)\), reduces to the form \(0\over 0\), then (x – a) is a factor of f(x) …

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Parametric Equation of all Forms of Parabola

Here you will learn what is the parametric equation of all forms of parabola and their parametric coordinates. Let’s begin – Parametric Equation of Parabola and Coordinates (i) For the parabola \(y^2\) = 4ax : The parametric equation is x = \(at^2\) & y = 2at. And parametric coordinates are (\(at^2\), 2at). (ii) For the …

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Pole and Polar of a Circle Equation

Here you will learn what is the pole and polar of a circle and pole of given line with respect to a circle. Let’s begin – Pole and Polar of a Circle Let any straight line through the given point A\((x_1, y_1)\) intersects the given circle S = 0 in two points P and Q …

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