Question

limx->0 ln2x/x^2+x
Urgenttttt va roggg!!!

Answer 1

[tex]\it ln\dfrac{2x}{x^2+x} = ln\left(2\cdot\dfrac{x}{x^2+x}\right) = ln2 +ln\dfrac{x}{x(x+1)} = ln2 +ln\dfrac{1}{x+1} \\\;\\ \\\;\\ \lim \limits_{x \to 0} ln \dfrac{1}{x+1} = ln \lim \limits_{x \to 0} \dfrac{1}{x+1} = ln1 = 0 \\\;\\ \\\;\\ \lim \limits_{x \to 0} ln\dfrac{2x}{x^2+x} = \lim \limits_{x \to 0} \left(ln2 +ln\dfrac{1}{x+1}\right) = ln2 + \lim \limits_{x \to 0} \left(ln\dfrac{1}{x+1}\right) = [/tex]

$\it = ln2 +0 = ln2.$