Limites e continuidade
Aula 3 e exercícios - Limites e o infinito
Aula com exemplos
Exercícios resolvidos
3.1) 
Calcule
cada um dos seguintes limites:
| (a) $\displaystyle\mathop {\lim }\limits_{x \to + \infty } \left( {10 + x} \right)$ | (b) $\displaystyle\mathop {\lim }\limits_{x \to - \infty } \left( {10 + x} \right)$ | (c) $\displaystyle\mathop {\lim }\limits_{x \to + \infty } \left( {9999 - 2x} \right)$ |
| (d) $\displaystyle\mathop {\lim }\limits_{x \to + \infty } \left( {{x^2} + 5{x^5}} \right)$ | (e) $\displaystyle\mathop {\lim }\limits_{x \to + \infty } \left( { - x - {x^2}} \right)$ |
3.2)
Calcule
cada um dos seguintes limites:
| (a) $\displaystyle\mathop {\lim }\limits_{x \to {2^ + }} \frac{1}{{x - 2}}$ | (b) $\displaystyle\mathop {\lim }\limits_{x \to {3^ - }} \frac{{ - 3}}{{3 - x}}$ | (c) $\displaystyle\mathop {\lim }\limits_{x \to {2^ - }} \frac{{2x}}{{{x^2} - 4}}$ |
| (d) $\displaystyle\mathop {\lim }\limits_{x \to {0^ + }} \frac{{5x + 2}}{{{x^2} - 3x}}$ | (e) $\displaystyle\mathop {\lim }\limits_{x \to {2^ - }} \frac{{4{x^2}}}{{2x - {x^2}}}$ | (f) $\displaystyle\mathop {\lim }\limits_{x \to {1^ + }} \frac{{\sqrt 2 - 2}}{{1 - {x^2}}}$ |
| (g) $\displaystyle\mathop {\lim }\limits_{x \to + \infty } \frac{{12}}{{1 - x}}$ | (h) $\displaystyle\mathop {\lim }\limits_{x \to - \infty } \frac{{2 - \ln {e^4}}}{{8 + x}}$ | (i) $\displaystyle\mathop {\lim }\limits_{x \to + \infty } {2^x}$ |
| (j) $\displaystyle\mathop {\lim }\limits_{x \to + \infty } {\left( {\frac{2}{3}} \right)^x}$ | (l) $\displaystyle\mathop {\lim }\limits_{x \to - \infty } {e^x}$ | (m) $\displaystyle\mathop {\lim }\limits_{x \to - \infty } \frac{5}{{{e^x} + x}}$ |