Question

Cum rezolv punctul 7?

Answer 1

Amplificam cu conjugata si apoi simplificam cu x: f(x)=$\frac{ (\sqrt[3]{1+x}-1)( \sqrt[3]{1+x}^2+ \sqrt[3]{x+1}+1) }{x( \sqrt[3]{1+x}^2+ \sqrt[3]{x+1}+1) }= \frac{1+x-1}{x( \sqrt[3]{1+x}^2+ \sqrt[3]{x+1}+1) }= \frac{1}{( \sqrt[3]{1+x}^2+ \sqrt[3]{x+1}+1) },$. Trecand la limita: $\lim_{x \to \ 0} f(x)= \frac{1}{1^2+1+1}= \frac{1}{3}.$