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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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 …
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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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) …
Here you will learn direct substitution method to solve limits with examples. Let’s begin – Direct Substitution Method to Solve Limits Consider the following limits : (i) \(lim_{x \to a}\) f(x) (ii) \(lim_{x \to a} {\phi(x)\over \psi(x)}\) If f(a) and \(\phi(a)\over \psi(a)\) exist and are fixed real numbers, then we say that \(lim_{x \to a}\) …
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 …
Here you will learn what is the formula to find the equation of radical axis of two circles. Let’s begin – Radical Axis of Two Circles Definition : The locus of a point, which moves in such a way that the length of tangents drawn from it to the circle are equal and is called …
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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 …
Here you will learn equation of chord of contact of circle and length of chord of contact of circle. Let’s begin – Equation of Chord of Contact A line joining the two points of contacts of two tangents drawn from a point outside the circle, is called chord of contact of that point. If two …
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Solution : We have, P(n, r) = \(n!\over (n – r)!\) Putting r = n, \(\implies\) P(n, n) = \(n!\over 0!\) \(\implies\) n! = \(n!\over 0!\) [ \(\because\) P(n, n) = n! ] \(\implies\) 0! = \(n!\over n!\) = 1 Hence, Proved.
