Recent content by theriel

Oh, that was much simpler than I expected... Once again, I am really impressed by the effort and time you spend for helping people solve their mathematical problems... Thank you very much for that! Greetings, Theriel

Sorry, I didn't get what you have said #-/. In my task I have to generalize my findings. I found that: For an odd function "f": f(-x)=-f(x) The derivative is even: f'(-x)=f'(x) And now the problem is how to prove it. Showing that only for the functions mentioned previously (x^2, tan(2x) etc.)...

Yeah, but the point is that later I will have to generalize and prove the situation. That is why I started doing that part, because proving it for these examples (f(2x), f(x^2) etc.) is easy ;-]. So... could you refer to my small problem in previous post, please?

So: There is an odd function: f(-x)=-f(x) We want to show that its derivative is even, hence: f'(-x)=f'(x) f'(x) = lim{h->0} (f(x+h) - f(x))/h f'(-x)=lim{h->0} ((f(-x+h) - f(-x))/h = lim{h->0} (f(-x+h) - f(x))/h The problem is how to show that: f(-x+h)=f(x+h) knowing that f(-x)=-f(x)... #-/

For functions: sin(1)=0.841 sin(-1)=-0.841 5x=5 5x=-5 4x^7 − 5x^3 + 8x=7 4x^7 − 5x^3 + 8x=-7 tan(2)=-2.185 tan(-2)=2.185 For derivatives: cos(1)=0.5403 cos(-1)=0.5403 5 5 28x^3-15x^2+8=21 28x^3-15x^2+8=21 2/cos^2x=11,55 2/cos^2x=11,55 Hence we see that when a function is symmetric about (0,0)...

Hello! I have a very interesting task, however, at the very beginning I should notice something but... I have a small problem with that ;-]. We have functions: ->sin x, ->5x ->4x7 − 5x3 + 8x ->tan(2x) I should find their common feature, then find their derivatives and check what do...

OK, I did what I said I would and... still, there is a problem. I got to the point, where: We know that there is somewhere an argument of this function which must have the same value as x=2. How to find it? I know I have to solve: sqrt(2) = x ^ (1/x) but... how? We may square sides and...

OK, I checked it. Using your way the result is the same (though more 'normally' looking at first glance).

That's the magic of this forum ;-]. Some special vibrations helped me ^^. Yeah, now the point is to justify it algebraically ;-]. So... First we check the monotonicity of the function x^(1/x). To do that, we need some bad-looking derivative of this function: f' =...

Noo... Sorry guys for making problem. The task is: Consider the numbers n^(1/n), n>=2. How many of them are equal? Justify your answer. I found the second approach. The function above is decreasing from e to infinity and tends to 0. Hence, the values between 2 and 'e' repeat. Hence, there might...

NateTG: What do you mean by the third root of 1 and -1 (sooo many ambiguities today...) The root of degree 3? For 1: 3rd: 1; -1/2 + i*sqrt(3); -1/2-i*sqrt(3), 4th: 1, i, -1, -i, For -1: 3rd: -1; 1/2- i*sqrt(3); 1/2+i*sqrt(3), 4th: [sqrt(2)+sqrt(2)i]/2; [-sqrt(2)+sqrt(2)i]/2...

I was just thinking about the task and maybe the problem is different... Like, how many numbers ARE EQUAL. Just plot the curve for "root of "x" of x degree", n >= 2. First, it is increasing TILL THE NUMBER x=e (is it a coincidence? I do not think so), then it is descending and tends to... 1...

Root of "n" degree of the number "n" Hello! Frankly speaking I am not sure whether this is proper forum, because I am not sure if this exercise involves calculus or not... The task is: Consider the numbers "root of "n" of n degree", n >= 2. How many of them are equal? Justify your answer...

Hello! I have just a small question - does the theory of polynomials say something about their coefficients? I mean: is the polynomial with all the coefficients being imaginary still considered as a "normal' polynomial?

Because there were no replies I decided to learn Latex... and I wrote the whole equation. Maybe now somebody can help me and check where the error is? P.S. I am sorry for the line breaking however it is not working properly, I do not know why...