integrating factor derivative

Introduction - Integration and differentiation are a pair of inverse operations. So far, from a given function, we have been finding its derivative but the question arises: what is the function whose derivative is known? If the derivative of a function is giv..

Introduction - During the course of study of Mathematics, we must have come across several parts of inverse operations like (addition, subtraction) (multiplication, division) (forming an equation whose roots are given - solving a given equation) and so on. In practical situations, we may be interes..

1. Both are operations on functions. 2. Both are linear. This is because of the following: (i) (ii) The constant can be taken outside the differential as well as integral sign as shown below: 3. We heve already seen that not all functions are differentiable. Similarly, all functions are n..

In (a + b) n , let 'a' and 'b' be both positive numbers. As r increases, the factor decreases. So long as this factor is greater than 1, T r+1 remains greater tha..

If several satellites are spaced around the same orbit in space, the tracks of the satellites will be different due to Earth's rotation about its own axis. But if, for example, four satellites are placed into different orbits with their ascending modes displaced successively by 30 intervals to the..

Alternative Proof of Binomial Theorem for Positive Integral Index (Combinatorial Method). We have, (a + b) n = (a + b) (a + b) ....... n times. The terms on the RHS are obtained by taking one letter from each factor and multiplying them together. Choosing 'a' from all the..

The expression, which when multiplied to a non-exact differential equation to convert it into exact differential equation is known as => A variable or A derivative or A factor or An integrating factor..

Derived growth factor which stimulates the mitosis of fibroblasts at the site of injury to fill in the damaged areas under the blood cl..

From the above two theorem, we infer the following (Anti derivative of the function f(x) at b) - (Anti derivative of the function f(x) at a) (ii) The fundamental theorem of integral calculus shows a close relationship between differentiation and integration..

Limits- operations on functions Continuity of a function Intermediate value, extreme value theorem Derivatives, differentiability Derivatives of functions Chain rule Rolle's theorem, mean value theorem, and L'Hopital's rule Maxima, minima, inflection points, intervals ..