Question

me ajudem a calcular esse limite:
lim (4 + t)² - 16
              t          quando t tende para 0

Answer 1

$\underset{t \to 0}{\mathrm{\ell im}}\,\dfrac{\left(4+t \right )^{2}-16}{t}$


Fazendo a mudança de variável

$u=4+t\;\;\Leftrightarrow\;\;t=u-4\\ \\ t \to 0\;\;\Leftrightarrow\;\;u \to 4$


chegamos a

$\underset{u \to 4}{\mathrm{\ell im}}\,\dfrac{u^{2}-16}{u-4}\\ \\ =\underset{u \to 4}{\mathrm{\ell im}}\,\dfrac{\left(u-4 \right )\left(u+4 \right )}{u-4}\\ \\ =\underset{u \to 4}{\mathrm{\ell im}}\,\left(u+4 \right )\\ \\ =4+4\\ \\ =8\\ \\ \\ \boxed{\underset{t \to 0}{\mathrm{\ell im}}\,\dfrac{\left(4+t \right )^{2}-16}{t}=8}$