1. Calclule os seguintes limites no infinito. (a) $\lim_{x ...

1. Calclule os seguintes limites no infinito.

(a) $\lim_{x \to +\infty} (x^4+3x+2)$ (b) $\lim_{x \to +\infty} (x^4-3x+2)$ (c) $\lim_{x \to +\infty} (3x^3+2x+1)$ (d) $\lim_{x \to +\infty} (3x^3+2x+1)$ (e) $\lim_{x \to +\infty} (5-4x+x^2-x^5)$ (f) $\lim_{x \to +\infty} (5-4x+x^2-x^5)$ (g) $\lim_{x \to +\infty} \frac{5x^3-6x+1}{6x^3+2}$ (h) $\lim_{x \to +\infty} \frac{5x^3-6x+1}{6x^3+2}$ (i) $\lim_{x \to +\infty} \frac{\sqrt{x+1}}{x+3}$ (j) $\lim_{x \to +\infty} (x-\sqrt{x+3})$ (k) $\lim_{x \to +\infty} (x-\sqrt{x+3})$ (l) $\lim_{x \to +\infty} (x-\sqrt{x^2+3})$ (m) $\lim_{x \to +\infty} (2x-\sqrt{x^3+3})$ (n) $\lim_{x \to -\infty} \frac{5-x}{3+2x}$ (o) $\lim_{x \to -\infty} \frac{2-\sqrt{x}}{\sqrt{1-x}}$

RESPOSTAS

| (a) | (b) | (c) | (d) | (e) | (f) | (g) | (h) | (i) | (j) | (k) | (l) | (m) | (n) | (o) | |---|---|---|---|---|---|---|---|---|---|---|---|---|---|---| | $\infty$ | $\infty$ | $\infty$ | -$\infty$ | -$\infty$ | $\infty$ | 5/6 | 5/6 | 0 | $\infty$ | 0 | -$\infty$ | -$\infty$ | -1/2 | -1 |

Limites Fundamentais

2. Calcule os limites.

(a) $\lim_{x \to 0} \frac{sen(3x)}{2x}$ (d) $\lim_{x \to 0} \frac{1-cos(x)}{x^2}$ (g) $\lim_{x \to 0} \frac{1-cos(x)}{x \cdot sen(x)}$ (j) $\lim_{x \to 0} \frac{\sqrt{1+sen(x)}-\sqrt{1-x}}{x}$ (b) $\lim_{x \to 0} \frac{sen(10x)}{sen(7x)}$ (e) $\lim_{x \to 0} \frac{1-sec(x)}{x^2}$ (h) $\lim_{x \to 0} \frac{7-7cos^2(x)}{3x^2}$ (k) $\lim_{x \to \infty} \frac{2x^3-x+sen(x)}{x^3}$ (c) $\lim_{x \to 0} \frac{tg(3x)}{2x}$ (f) $\lim_{x \to 0} \frac{1-cos(x)}{x}$ (i) $\lim_{x \to x_0} \frac{sen(x)}{x-x_0}$ (l) $\lim_{x \to 0} \frac{sen(x+a)-sen(a)}{x}$

3- Calcule os limites:

(a) $\lim_{x \to \infty} (1+\frac{1}{x})^x$ (c) $\lim_{x \to \infty} (1+\frac{1}{x})^{3x}$ (e) $\lim_{x \to \infty} (1+\frac{1}{x})^{x^2}$ (g) $\lim_{x \to \infty} (\frac{x}{x+1})^x$ (b) $\lim_{x \to \infty} (1-\frac{1}{x})^x$ (d) $\lim_{x \to \infty} (1-\frac{1}{x})^{5x}$ (f) $\lim_{x \to \infty} (\frac{x}{x+1})^{x+1}$ (h) $\lim_{x \to \infty} (\frac{x}{x+5})^{2x+3}$

4. Determine:

(a) $\lim_{x \to 0} \frac{e^x-1}{2x}$ (b) $\lim_{x \to \infty} \frac{3^{1/x}-3}{x}$ (c) $\lim_{x \to 3} \frac{x^4-64}{x-3}$ (d) $\lim_{x \to \infty} \frac{4-e^x}{x}$