The limit of an integral that depends on x for f(t)=e^1/ln(t) with x going to infinity.

The limit of an integral that depends on x for f(t)=e^1/ln(t) with x going to infinity.
We will prove the mean value of theorem for integrals. But first, we're going to prove, Or we cannot remind ourselves of the mean value. Theorem for derivatives, in fact, to the mean value theorem says that if f is defined on some bounded interval, A B continuous and differentiable on the interval North, including the boundaries of the interval. Then there is some C in that interval North, including the boundaries Such that F. Prime of C, the derivative of f at c is equal to F of B minus F of Over. B, minus a, The mean value theorem is very important improving results and it's one of the most fundamental theorem in, in calculus, it helps us prove more result that we can imagine. We're going to use the mean value, theorem for integrals, to find the average value for integrals. We will find the particular C that will help us find the value that we get in. Need the mean value theorem for integrals. Let us find limits that we can do Directly by computation. It's very useful when dealing with limits that we can't compute. It's similar to the mean value theorem for. Derivatives the mean value theorem for integrals is very important and very useful. Here we present a proof of it. We're going to give some geometrical explanation for it and also we can see what we think of it as a theorem in general. This is one of the key elements that we're gonna need improving the artificial results in. Uh, Deeding with integrals, it's various form. We're going to apply it in solving some problems or give two or three examples of it and we're gonna apply it and we're gonna see one to deal with it and how to use it. Be careful. This is one of the most beautiful results that you will see when you're trying to solve some theratical results.
#python #maths #calculus