Recent content by scientifico

Hi, I've read that the speed of em waves in the vacuum is the electric field component frac the magnetic field component, why and how can this be explained more easily ? Thanks

So why the base changing formula is valid for a variable base too ?

But why that formula doesn't work ?

Homework Statement Hello, I have to calculate the derivative of y = log_x (x+1) so I used the formula of the derivative of a n-base logarithm and I get y' = 1/((x+1)logx) but that's wrong, why ? Thanks Homework Equations log_a x = 1/(xlog(a))

I've set up this unequation \frac{x-3}{x-1} < - M to prove the limit using its definition but it doesn't lead to the result 1<x<1+\frac{2}{M+1}

Homework Statement Hello, I have to prove, using the limit definition, that \lim_{x\to 1^{+}}{\frac{x-3}{x-1}}=-\infty The Attempt at a Solution I've set this unequation \frac{x-3}{x-1} < - M but it doesn't lead to the result 1<x<1+\frac{2}{M+1}, what did I wrong ? Thanks

In that cases you simplified for x, how can I rewrite e^{1/x}3x^2 to simplify it ?

I mean \lim_{x\to c}{f(x)\cdot g(x)} = \lim_{x\to c}{f(x)}\cdot\lim_{x\to c}{g(x)} Why they must be finite and anyway what allow me to ignore the other limit in case it isn't ?

I still can't understand Taylor series, I just would like to know why in this case the limit product rule doesn't work (ok for the infinity grade but shouldn't it work with as a product too ? )

Hello, why lim_{x\to (0)^{+}}e^{1/x}3x^2 = +\infty if lim_{x\to (0)^{+}}e^{1/x} = \infty and \lim_{x\to (0)^{+}}{3x^{2}} = 0 shouldn't it be +\infty * 0 ? I can't get it :( Thanks

What you mean ?

I mean why you can't solve it directly but you have to factorize it since the original trinomial and its factorization are the same thing

Ok but how do I get a^2 - b^2 + ab - ab from a^2 - b^2 ?

Hello, how can I prove using factorization that a^2 - b^2 = (a+b)(a-b) ? a*a - b*b I should get something like a(a-b)+b(a-b) but how ? thanks

Why not all trinomials (for example x^2+3x-15) can be written as (x+a)(x+b) ?