Aula 5 - Limites notáveis com exponenciais e logaritmos
● Exercícios em vídeo
5.1) Calcule cada um dos seguintes limites:
 (a) $\displaystyle\mathop {\lim }\limits_{x \to 0} \frac{{{e^x} - 1}}{{2x}}$; |
(b) $\displaystyle\mathop {\lim }\limits_{x \to 0} \frac{{1 - {e^{3x}}}}{{2x}}$; |
(c) $\displaystyle\mathop {\lim }\limits_{x \to 0} \frac{{{e^{ - x}} - 1}}{x}$; |
| (d) $\displaystyle\mathop {\lim }\limits_{x \to 0} \frac{{{e^x} - {e^{5x}}}}{{2x}}$; |
(e) $\displaystyle\mathop {\lim }\limits_{x \to 0} \frac{{{e^x} - 1}}{{{e^{2x}} - 1}}$; |
(f) $\displaystyle\mathop {\lim }\limits_{x \to 3} \frac{{{e^x} - {e^3}}}{{x - 3}}$; |
| (g) $\displaystyle\mathop {\lim }\limits_{x \to + \infty } {e^x}$; |
(h) $\displaystyle\mathop {\lim }\limits_{x \to + \infty } {\pi ^x}$; |
(i) $\displaystyle\mathop {\lim }\limits_{x \to - \infty } {e^{3x}}$; |
| (j) $\displaystyle\mathop {\lim }\limits_{x \to + \infty } {\left( {\frac{2}{3}} \right)^x}$; |
(l) $\displaystyle\mathop {\lim }\limits_{x \to + \infty } \frac{{{2^x}}}{{{e^x}}}$; |
(m) $\displaystyle\mathop {\lim }\limits_{x \to - \infty } \frac{{{2^x}}}{{{e^x}}}$; |
| (n) $\displaystyle\mathop {\lim }\limits_{x \to + \infty } \frac{{{e^x}}}{{2x}}$; |
(o) $\displaystyle\mathop {\lim }\limits_{x \to + \infty } \frac{{{e^{2x}}}}{{{x^3}}}$; |
(p) $\displaystyle\mathop {\lim }\limits_{x \to + \infty } \frac{x}{{{e^{2x}}}}$. |
Rui
5.2) Calcule cada um dos seguintes limites:
| (a) $\displaystyle\mathop {\lim }\limits_{x \to 0} \frac{{\ln {{\left( {x + 1} \right)}^2}}}{{4x}}$; |
(b) $\displaystyle\mathop {\lim }\limits_{x \to 0} \frac{{\ln \left( {2x + 1} \right)}}{{3x}}$; |
(c) $\displaystyle\mathop {\lim }\limits_{x \to \frac{1}{2}} \frac{{\ln \left( {2x} \right)}}{{2x - 1}}$; |
| (d) $\displaystyle\mathop {\lim }\limits_{x \to + \infty } \frac{{\ln \left( {2x} \right)}}{x}$; |
(e) $\displaystyle\mathop {\lim }\limits_{x \to - \infty } \frac{{\ln \left( { - 3x} \right)}}{x}$; |
(f) $\displaystyle\mathop {\lim }\limits_{x \to - \infty } \frac{{{x^5}}}{{\ln \left( { - x} \right)}}$; |
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