Limites e continuidade

Aula 3 - Limites e o infinito

● Exercícios em vídeo

Vídeo 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) $\displaystyle\mathop {\lim }\limits_{x \to  + \infty } \left( { - x - {x^2}} \right)$  

 

Vídeo 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) $\displaystyle\mathop {\lim }\limits_{x \to  - \infty } \frac{5}{{{e^x} + x}}$

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