What is Induction in math? Mathematical induction is a special method or technique to prove the statements given in consideration. Generally, it is used to prove the statements of the set of natural numbers.Principle of Mathematical Induction: Mathematical induction is used to prove that the given statement is true or not. It uses 2 steps Read more about Principle of Mathematical Induction[…]
Direct Common Tangents: The direct common tangents to two circles meet on the line of centers and divide it externally in the ratio of the radii. The transverse common tangents also meet on the line of centers and divide it internally in the ratio of the radii Now we discuss the number of common tangents that exist for the cases Read more about Common Tangents[…]
A relation is a function if for every x in the domain there is exactly one y in the codomain An example If A = {1, 2, 3} and B = {a, b, c}, f = {(1, a), (2, b), (3, c)}. Then f is a function from A to B. Example: If A = {a₁, Read more about Function […]
Complex Numbers: The numbers of the form x +iy are known an complex numbers .here x and y real numbers and i = √-1 is iota.A complex number may also defines as an ordered pair of real numbers and it is denoted by symbol (x, y). Where x is called real part and y is Read more about Conjugate of A Complex Numbers[…]
Tangent to the circle: Circle is a line that touches the circle at exactly one point is called tangent to the circle (or) A tangent to a curve at a point is a straight line that touches the curve at that point.Equation of tangent: The equation of the tangent at p(x₁, y₁) of the circle S = 0 Read more about Tangent and Normal[…]
A simple formula for calculating power of complex numbers in the form of cosθ and sinθ is known as de-moivre’s theorem. The De-moivre’s theorem. If n is integer (cosθ + isinθ)n = (cosnθ + isinnθ) Cube Roots of Unity: Let us the cube roots of z is 1 Z = 3√ (1) Z³ = 1 Z³ Read more about De – Moivre’s Theorem[…]
Let f be a relation from A into B then {x ϵ A: (x, y) ϵ R} is codomain of f and {y ϵ B: (x, y) ϵ f} is called range of f Domain: The domain is input values Range: The resultant value is called range Ex: if f = {(a, b), (c, d), Read more about Domain, Co – Domain and Range[…]
A locus is a set of points which satisfy certain geometric conditions. Many geometric shapes are most naturally and easily described as locus. For example, a circle is the set of points in a plane which are a fixed distance from a given point the center of the circle. Example: A locus The following diagrams give the locus of a Read more about Locus[…]
A first order and first degree differential equation involves the independent variable x (say), dependent variable y (say) so, it can be put in any one of the following forms: dy/ dx = f(x, y) or f (x, y) = 0, or f(x, y) dx + g(x, y)dy = 0 Where f(x, y) and g(x, Read more about First order and first degree differential equations and their geometrical interpretations[…]
Consider a family of exponential curves (y = Aex), where A is an arbitrary constant for different values of A, we get different members of the family. Differentiating the relation (y = Aex) w.r.t.x, we get dy/dx = Aex Eliminating the arbitrary constant between y = Aex and dy/dx = Aex, we get dy/dx = Read more about Formation of differential equations[…]