Question

Найдите все значения x, для которых v'(x) +v (x) = 1/x _v(1/x), если v(x)= lnx

Answer 1

1) v'(x)=1/x, значит: v'(x)+v(x)=1/x-v(1/x) <=> lnx=-lx(1/x) - решений нет

Answer 2

To find all the values of x that satisfy the given expression, we first need to compute v'(x) and v(1/x).

Given that v(x) = ln(x), we can find v'(x) by taking the derivative of ln(x) with respect to x:

v'(x) = d/dx(ln(x)) = 1/x.

Next, we need to compute v(1/x). We substitute x with 1/x in the expression for v(x):

v(1/x) = ln(1/x) = ln(1) - ln(x) = 0 - ln(x) = -ln(x).

Now, we have the expression v'(x) + v(x) = 1/x - ln(x).

So, we need to solve the equation:

1/x - ln(x) = -ln(x).

Let's simplify the equation:

1/x = 0.

Now, we can see that there is no value of x that satisfies this equation. Dividing any number (except 0) by 0 is undefined, and hence, there are no valid solutions for this expression.

Thus, the answer is that there are no values of x that satisfy the given expression v'(x) + v(x) = 1/x - ln(x) _v(1/x) when v(x) = ln(x).