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Can you please show that first derivation is piecewise continuous?
gp2772
Assuming you mean "derivative", I believe it really depends on the function. In the general case, there is no guarantee that the first derivative is piecewise continuous, or that it is even defined.
Wiki User
∙ 7y ago
Wiki User
∙ 6y agoIt is not possible to show it because for many functions, it may not be true.
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What is the meaning of continuous first derivatives of a function?
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what is differential equation?
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.
Give exampal of function continuous everywhere but not derivable any where?
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.
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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?
