Lımites trigonometricos

7. Límites trigonométricos

Ejercicio 8.1

Calcule

1: $lim_{x \to 0} \frac{x^{2} + x sen x}{cos x - 1}$
$- 4$ .
2: $lim_{t \to 0} \frac{t - sen (2 t)}{t + sen (3 t)}$
$\frac{- 1}{4}$ .
3: $lim_{n \to 0} \frac{1 - {cos}^{3} n}{{sen}^{2} n}$
$\frac{3}{2}$ .
4: $lim_{x \to 1} \frac{sen (x - 1)}{\sqrt{x} - 1}$
$2 .$
5: $lim_{y \to 0} \frac{tan y - sen y}{{sen}^{3} y}$
$\frac{1}{2}$ .
6: $lim_{a \to 0} \frac{\sqrt{2} - \sqrt{1 + cos a}}{{sen}^{2} a}$
$\frac{\sqrt{2}}{8}$ .
7: $lim_{z \to 0} \frac{sec (2 z) \cdot tan (3 z)}{4 z}$
$\frac{3}{4}$ .
8: $lim_{y \to 0} \frac{sec y - 1}{y^{3} csc y}$
$\frac{1}{2}$ .
9: $lim_{x \to 0} \frac{{tan}^{2} x + x^{2} cos x}{x tan x}$
$2 .$
10: $lim_{z \to 0} \frac{tan (3 z)}{8 z cos z}$
$\frac{3}{8}$ .
11: $lim_{x \to 1^{+}} ln (\frac{4}{sen (3 x - 3)})$
$\infty$ .
12: $lim_{z \to 0} \frac{sen z - tan z}{z^{2} \cdot sen (2 z)}$
$\frac{- 1}{4}$ .
13: $lim_{t \to 0^{-}} \frac{sen (2 t)}{2 cos (2 t) - 2}$
$\infty$ .
14: $lim_{x \to {\frac{π}{2}}^{-}} [{(\frac{π}{4})}^{\frac{7}{tan (x)}} \cdot \frac{sen (2 x - 3 π)}{2 x - π}]$
$1 .$
15: $lim_{t \to - 4 π ∕ 3} \frac{sen t}{t}$
$\frac{- 3 \sqrt{3}}{8 π} \approx - 0, 206748$ .
16: $lim_{w \to π ∕ 4} \frac{sen w - cos w}{1 - tan w}$
$\frac{- \sqrt{2}}{2}$ .
17: $lim_{x \to π ∕ 2} \frac{cot x cos x}{1 - sen x}$
$2 .$
18: $lim_{β \to 0} \frac{sen 5 β}{β}$
$5 .$
19: $lim_{z \to 0} \frac{5 {sen}^{2} (3 z)}{2 z^{2}}$
$\frac{45}{2}$ .
20: $lim_{u \to 0^{+}} \frac{\sqrt{u}}{sen u}$
$\infty$ .
21: $lim_{y \to 1} \frac{y^{2} - 1}{sen (πy)}$
$\frac{- 2}{π} \approx - 0, 636620$ .
22: $lim_{x \to 0} {(\frac{2}{7})}^{cot | x |}$
$0 .$
23: $lim_{α \to π} \frac{1 - sen (α ∕ 2)}{π - α}$
$0 .$
24: $lim_{x \to - π ∕ 6} \frac{tan (x + π ∕ 6)}{6 x + π}$
$\frac{1}{6}$ .
25: $lim_{β \to 5 π ∕ 6} 3 sen β - 2 cos β$
$\frac{3}{2} + \sqrt{3} \approx 3, 23205$ .
26: $lim_{β \to π ∕ 2} sen (cos β) se c^{2} β$
$\infty$ izquierda, $- \infty$ derecha.
27: $lim_{w \to 0} (\frac{sec (w) - 1}{w^{2} csc (w)})$
0.
28: $lim_{u \to a} \frac{sen u - sen a}{u - a}$ con $a$ constante
$cos a$ .
29: $lim_{u \to a} \frac{cos u - cos a}{u - a}$ con $a$ constante
$- sen a$ .

Siguiente →← Anterior ⌂ Inicio