Limites e continuidade
Aula 4 e exercícios - Limites e indeterminações
Aula com exemplos
Exercícios resolvidos
4.1) 
Calcule cada um dos seguintes limites:
| (a) $\displaystyle\mathop {\lim }\limits_{x \to + \infty } \left( {{x^5} + 3x + 2} \right)$; | (b) $\displaystyle\mathop {\lim }\limits_{x \to + \infty } \left( {{x^5} - 3x + 2} \right)$; | |
| (c) $\displaystyle\mathop {\lim }\limits_{x \to - \infty } \left( {4{x^5} - 3x - {x^6}} \right)$; | (d) $\displaystyle\mathop {\lim }\limits_{x \to - \infty } \left( {9x - 42{x^2} - 2{x^3}} \right)$ | |
| (e) $\displaystyle\mathop {\lim }\limits_{x \to + \infty } \frac{{3 + 7x}}{{2 - x}}$ | (f) $\displaystyle\mathop {\lim }\limits_{x \to - \infty } \frac{{2{x^2} + 5x}}{{{x^2} + 3x + 2}}$ | |
| (g) $\displaystyle\mathop {\lim }\limits_{x \to - \infty } \frac{{{x^2}}}{{{x^3} + 9}}$ | (h) $\displaystyle\mathop {\lim }\limits_{x \to - \infty } \left( {\frac{1}{{{x^2}}} \times \frac{{{x^5}}}{{4 - 2x}}} \right)$ |
4.2)
Calcule cada um dos seguintes limites:
| (a) $\displaystyle\mathop {\lim }\limits_{x \to + \infty } \left( {\sqrt {x - 3} - \sqrt x } \right)$ | (b) $\displaystyle\mathop {\lim }\limits_{x \to + \infty } {\frac{{\sqrt {3x} - \sqrt {7 + 3x} }}{2}} $ | ||
| (c) $\displaystyle\mathop {\lim }\limits_{x \to - \infty } {\frac{4}{{\sqrt {1 - 2x} - \sqrt {3 - 2x} }}} $ | (d) $\displaystyle\mathop {\lim }\limits_{x \to - \infty } {\frac{{\ln \sqrt e \times {x^2}}}{{\sqrt {{x^2}} - \sqrt {5 + 4{x^2}} }}} $ |
4.3)
Calcule cada um dos seguintes limites:
| (a) $\displaystyle\mathop
{\lim }\limits_{x \to 2} \frac{{{x^2} - 4}}{{x - 2}}$; |
(b) $\displaystyle\mathop
{\lim }\limits_{x \to - 1} \frac{{{x^3} + 1}}{{x + 1}}$; |
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| (c) $\displaystyle\mathop
{\lim }\limits_{x \to 2} \frac{{{x^3} - 5{x^2} + 8x - 4}}{{2{x^3} - 6{x^2} + 8}}$; |
(d) $\displaystyle\mathop
{\lim }\limits_{x \to {1^ + }} \frac{{{x^3} - 6{x^2} + 11x - 6}}{{{x^3} + {x^2} - 5x + 3}}$; |
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| (e) $\displaystyle\mathop
{\lim }\limits_{x \to {0^ + }} \frac{{{x^4} + {x^2}}}{{{x^3}}}$; |
(f) $\displaystyle\mathop
{\lim }\limits_{x \to {1^ + }} \frac{{{x^3} - 6{x^2} + 11x - 6}}{{{x^3} + {x^2} - 5x + 4}}$; |
||
| (g) $\displaystyle\mathop
{\lim }\limits_{x \to 0} \frac{x}{{\sqrt x }}$; |
(h) $\displaystyle\mathop
{\lim }\limits_{x \to 1} \frac{{x - 1}}{{\sqrt x - 1}}$; |
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| (i) $\displaystyle\mathop
{\lim }\limits_{x \to {0^ + }} \frac{{x - \sqrt x }}{{{x^3} - {x^2}}}$; |
(j) $\displaystyle\mathop
{\lim }\limits_{x \to - 3} \frac{{1 - \sqrt {x + 4} }}{{x + 3}}$. |