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 \(lim_{x \to a}\) […]
Direct Substitution Method to Solve Limits Read More »
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
Parametric Equation of all Forms of Parabola Read More »
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
Radical Axis of Two circles – Definition and Formula Read More »
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
Pole and Polar of a Circle Equation Read More »
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
Chord of Contact of Circle – Length and Equation Read More »
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.
Prove that value of zero factorial is 1. Read More »
Here you will learn what is composition of functions with properties and examples. Let’s begin – What is Composition of Functions ? Let f : A \(\rightarrow\) B & g : f : B \(\rightarrow\) C be two functions. Then the function gof : f : A \(\rightarrow\) C defined by (gof)(x) = g(f(x)) \(\forall\)
What is Composition of Functions ? Read More »
Here you will learn what is into function with definition and examples. Let’s begin – Into Function Definition Definition : A function f : A \(\rightarrow\) B is said to be an into function if every element of B having no pre-image in A. In other words, f : A \(\rightarrow\) B is an into
Into Function – Definition and Examples Read More »
Here you will learn what is onto function with definition and examples. Let’s begin – Onto Function (Surjection) Definition Definition : A function f : A \(\rightarrow\) B is said to be an onto function if every element of B is the f-image of some element of A i.e. , if f(A) = B or
Onto Function (Surjection) -Definition and Examples Read More »
Here you will learn what is many one function with definition and examples. Let’s begin – Many One Function Definition : A function f : A \(\rightarrow\) B is said to be a many-one function if two or more elements of set A have the same image in B. Thus, f : A \(\rightarrow\) B
Many One Function – Definition and Examples Read More »
