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A continuous function is one where there are no discontinuities or step changes in the function, i.e. for a small change in input value, as that small change approaches zero, there is a progressively smaller change in output value. There are many definitions, some formal and some intuitive, for continuous functions. The definition given above is intuitive. The same definition can be give to the deriviatives or the integrals of a function. Continousness does not depend on being a deriviative or integral.
The first derivative of position calculates instantaneous speed. If you do not know how to differentiate, then either use a calculator, use slope on the graph (if it's linear or piecewise-linear), or learn how... The derivative according to Newton is the limit as h approaches 0 of (f(x+h)-f(x))/h, and according to Leibniz it's the limit as x approaches a of (f(x)-f(a))/(x-a).
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A differential equation have a solution. It is continuous in the given region, but the solution of the impulsive differential equations have piecewise continuous. The impulsive differential system have first order discontinuity. This type of problems have more applications in day today life. Impulses are arise more natural in evolution system.
Randy Adams of Spur Tx has the first known usable continuous portable mixer
These devices were first used to harness WIND power to grind grain on a MILL stone.
Differential equation is defined in the domain except at few points (may be consider the time domain ti ) may be (finite or countable) in the domain and a function or difference equation is defined at each ti in the domain. So, differential equation with the impulsive effects we call it as impulsive differential equation (IDE). The solutions of the differential equation is continuous in the domain. But the solutions of the IDE are piecewise continuous in the domain. This is due to the nature of impulsive system. Generally IDE have first order discontinuity. There are so many applications for IDE in practical life.
Differential equation is defined in the domain except at few points (may be consider the time domain ti ) may be (finite or countable) in the domain and a function or difference equation is defined at each ti in the domain. So, differential equation with the impulsive effects we call it as impulsive differential equation (IDE). The solutions of the differential equation is continuous in the domain. But the solutions of the IDE are piecewise continuous in the domain. This is due to the nature of impulsive system. Generally IDE have first order discontinuity. There are so many applications for IDE in practical life.
I think the following piecewise function satisfies the two criteria: when x is rational: f(x)=x when x is irrational: f(x)=x*, where x* is the largest rational number smaller than x. I think not. When x is irrational, there is no largest rational number less than x. No matter what rational number you pick, there is a larger one that is less than x. For example, between 3.1415926 and pi, there is 3.14159265. The usual answer is the one given by Weierstrass, which is the sum of an infinite series of functions. The first term in the series is a periodic sawtooth (piecewise linear) function, which is = x from x=0 to x=1, and then descends back to 0 between x=1 and x=2 (i.e., it is = -x+2 in that interval). It repeats that pattern between x=2 and x=4, and so on. The second term is just like it, but with 1/10 the frequency and 1/10 the amplitude, and so on. The first function is continuous everywhere and differentiable except at x= an integer. The sum of the first 2 is continuous everywhere and differentiable except for the multiples of 1/10, and so on. It turns out that the series converges to a function that is continuous everywhere and differentiable nowhere. By the way, if you can take the derivative of a function at a given point, it is said to be differentiable, not derivable at that point.
Please please me was there first No. 1 hit.
The title of the beatles first album is, please please me released in 1963
In England, their native homeland, it was the album Please Please Me. In the USA it was "Meet The Beatles" which was pieced together from album tracks from Please Please Me, With The Beatles, and some of their singles.
DBYN:If in any derivation we replace the variables starting from the left side then it is called leftmost derivation in automata.let us take an example:consider the following production set--S->aBCB->ccaC->aBThen the leftmost derivation is as below:S=>aBC=>accaC[replacing variable B by cca]=>accaaB[replacing variable C by aB]=>accaacca[replacing variable B by cca]first time i don't have to logged in,i just click on answer it & share as much as i know,but in the 2nd time i have to logged in in order to improve the answer.Anyone knows why is that?
The parallelogram law of forces says that the sum of two forces is equivalent to the parallelogram formed by placing the first vector as starting from the origin and the second starting from the head of the first. This can be proven through trigonometric derivation of triangle angles and sides.
Please, Please Me