Recent content by dapet

By Newton Integral I mean the integral of f(x) dx from a to b defined as follows, let F be a primtive function to f then the discussed integral is equal to F(b) - F(a) or [lim (x --> b-) F(x) - lim (x --> a+) F(x)] and the Riemanns definition of integral is based on the areas in the graph. So...

Hi, I need a help with responding one question from my calculus classes... Lef f: [0, + infin.) ---> R be a continuous function and let exist the finite Newton integral of f(x) dx from 0 to +infinity. It´s neccesary that f is bounded? Thanks for any help. :wink:

Thank you...

I think that the maximum looks like: 40+(39/20)+(38/21)+...(30/29)-(1*18)-(2*17)-...-(10*9)-19 and the generalization is (according to my opinion) similar... It's easy to prove that numbers 40,39,...,30 must be in numerators of fractions for reach the maximum, but I don't know how to prove that...

There is a problem (the solution should use limit probability statements): One medical company invented some pills that should accelerate the growth of hair. The company wanted to try the pills on people - and so 2 groups of volunteers (each had 100 persons) were chosen to participate in the...

Yes, you're right... in base ten.

"sum of digits" equation Let f(n) denote the sum of (all) digits of natural number n. Prove that for each natural n we can choose convenient value of natural parameter p such that the equation f(npx)=f(x) has solution in natural numbers x that doesn't contain any "9" in its notation. Does...

Determine the permutation (x_1,x_2,...,x_40) of numbers 1,2,...,40 such that the expression x_1 + x_2 / x_3 - x_4 * x_5 + x_6 / x_7 - x_8 * x_9 + ... + x_38 / x_39 - x_40 has the maximal possible value. (the operators +,/,-,* alternate regularly.) It can be generalized for 4n (where n is an...

Let's imagine two sets A = {1,2,...,k} and B = {-1,-2,...,-k} for some natural k, then let's create n two-element sets X_1,X_2,...,X_n such that for each 0<i=<n X_i = {a,b} where a is from A and b is from B but |a|<>|b|. We know how do sets X_i look like and according to this we will choose the...