Question

Determinar o valor do limite a seguir Lim x^3-1/x-1, com x tendendo pra 1.

Answer 1

$\underset{x \to 1}{\mathrm{\ell im}}\,\dfrac{x^{3}-1}{x-1}\\ \\ =\underset{x \to 1}{\mathrm{\ell im}}\,\dfrac{\left(x-1\right)\cdot \left(x^{2}+x+1\right)}{x-1}\\ \\ =\underset{x \to 1}{\mathrm{\ell im}}\left(x^{2}+x+1\right)\\ \\ =\left(1\right)^{2}+\left(1\right)+1\\ \\ =1+1+1\\ \\ =3\\ \\ \\ \boxed{\underset{x \to 1}{\mathrm{\ell im}}\,\dfrac{x^{3}-1}{x-1}=3}$