Differentiation – Some Standard Substitutions Expression Substitution x = asinθ (or) acosθ x = atanθ (or) a cotθ x = asecθ (or) acosecθ (or) x = acosθ (or) acos2θ (or) x = acos²θ + b sin²θ Example: If , then prove that . Solution: Given that, , Let x³ = cosp and y³ = cosq Read more about Differentiation – Some Standard Substitutions[…]
Consortium of Medical, Engineering and Dental Colleges of Karnataka (COMEDK) 2020 Exam Date Released The Hon’ble Supreme Court in TMA Pai Foundation Vs. the State (2002) 8 SCC 481, Islamic Academy of Education Vs. the State reported in (2003) 6 SCC 697 and PA Inamdar Vs. the State of Maharashtra reported in (2005) 6 SCC Read more about Consortium of Medical, Engineering and Dental Colleges of Karnataka (COMEDK) 2020 Exam Date Released[…]
Non-Removable Discontinuity If , then f(x) is said to have the first kind of non-removable discontinuity. Consider the function f(x) = 1/x. the function is not defined at x = 0. It cannot be extended to a continuous function whose domain is R. since no matter what value is assigned at 0, the resulting function Read more about Non-Removable Discontinuity[…]
Velocity of Longitudinal Wave 1) Velocity of Sound in any Elastic Medium: It is given by . a) In solids, ; Where Y = Young’s modulus of elasticity. b) In a liquid and gaseous medium, ; where B = Bulk modulus of elasticity of liquid or gaseous medium. c) As solids are most elastic while Read more about Velocity of Longitudinal Wave[…]
Removable Discontinuity necessarily exists, but is either not equal to f(a) or f(a) is not defined. In this case, it is, possible to redefine the function in such that a manner that and thus, make the function continuous. Consider the function g(x) = (sin x)/x. the function is not defined at x = 0. So, Read more about Removable Discontinuity[…]
Velocity of Transverse Wave In a transverse wave the particle displacement is perpendicular to the direction of wave propagation. The velocity of a transverse wave in a stretched string is: . Where, T = Tension in the string, m = Linear density of string. 1) If A is the area of cross section of the Read more about Velocity of Transverse Wave[…]
Functional Equations Functional equation is any equation that specifies a function in implicit form. Often, the equation relates the value of a function (or functions) at some point with its values at other points. For instance, the properties of functions can be determined by considering the types of functional equations the satisfy. Functional equations satisfied Read more about Functional Equations[…]
Christian Medical College Post Graduation (CMC PG) 2020 Application Started All candidates are aware of the objectives of the Christian Medical College Vellore, which is “the establishment, maintenance and development of a Christian Medical College and Hospitals in India, where women and men shall receive an education of the highest grade in the art and Read more about Christian Medical College Post Graduation (CMC PG) 2020 Application Started[…]
General and Particular Solution of a Differential Equation We have solved the equation of the type: x² + 1 = 0 … (1) sin²x – cosx = 0 … (2) solution of equation (1) and (2) are numbers, real or complex, that will satisfy the given equation i.e., when that number is substituted for the Read more about General and Particular Solution of a Differential Equation[…]
Diffraction of Light The phenomenon of diffraction was first discovered by Girmaldi. Its experimental study was done by Newton’s and young. The theoretical explanation was first given by Fresnel’s. 1) The phenomenon of bending of light around the corners of an obstacle/ aperture of the size of the wave length of the light is called Read more about Diffraction of Light[…]