Explicație pas cu pas:
[tex]\lim _{x \rightarrow 0} \frac{3 {x}^{3} - 3x}{2 {x}^{2} } = \frac{3}{2}\lim _{x \rightarrow 0} \frac{x( {x}^{2} - 1)}{ {x}^{2} } \\ = \frac{3}{2} \lim _{x \rightarrow 0} \frac{ {x}^{2} - 1}{x} = \frac{3}{2} \lim _{x \rightarrow 0}\left( x - \frac{1}{x}\right)[/tex]
sunt două cazuri:
[tex]\frac{3}{2} \lim _{x \rightarrow {0}^{ + } }\left(x - \frac{1}{x}\right) = \frac{3}{2}(0 - \infty) = - \infty \\ [/tex]
[tex]\frac{3}{2} \lim _{x \rightarrow 0^{ - } }\left(x - \frac{1}{x}\right) = \frac{3}{2}(0 + \infty) = + \infty \\ [/tex]
