Limites trigonométricos
En los problemas del 1 al 22 hallar el límite indicado.
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\[ \lim\limits_{ x \rightarrow \pi } \frac{\text{sen } x}{x - \pi} \]
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\[ \lim\limits_{ x \rightarrow 0 } \frac{\text{sen } 2x}{\text{sen } 3x} \]
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\[ \lim\limits_{ x \rightarrow 0 } \frac{1 - \cos 2x}{4 x^2} \]
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\[ \lim\limits_{ x \rightarrow \pi/4 } [ \tan 2x - \sec 2x ] \]
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\[ \lim\limits_{ t \rightarrow 0 } \frac{1 - \cos t}{\text{sen } t} \]
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\[ \lim\limits_{ x \rightarrow 0 } \frac{\text{sen }^2 \left( \frac{x}{2} \right) }{\text{sen } x} \]
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\[ \lim\limits_{ x \rightarrow 1 } \frac{ \text{sen }^2 (x-1) }{ x^2 - 2x + 1 } \]
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\[ \lim\limits_{ x \rightarrow 0 } \frac{ x - \text{sen } 2x }{ x - \text{sen } 3x } \]
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\[ \lim\limits_{ x \rightarrow 0 } \frac{ \tan x - \text{sen } x }{ x^3 } \]
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\[ \lim\limits_{ x \rightarrow \pi/3 } \frac{ 1 - 2 \cos x }{ \pi - 3x } \]
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\[ \lim\limits_{ x \rightarrow \pi/4 } \frac{ \cos x - \text{sen } x }{ \cos 2x } \]
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\[ \lim\limits_{ x \rightarrow 0 } \frac{ \sqrt{2} - \sqrt{1 + \cos x} }{ \text{sen }^2 x } \]
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\[ \lim\limits_{ x \rightarrow 1 } \frac{ \cos \frac{\pi}{2} x }{ 1 - \sqrt{x} } \]
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\[ \lim\limits_{ x \rightarrow 0 } \frac{ 1 - \cos \sqrt{\cos x} }{x^2} \]
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\[ \lim\limits_{ x \rightarrow \pi/2 } \frac{ 1 - \text{sen } x } { \left(x - \frac{\pi}{2} \right)^2 } \]
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\[ \lim\limits_{ \theta \rightarrow 0 } \frac{ (1 - \cos \theta)^2 }{ \tan^5 \theta - \tan^3 \theta } \]
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\[ \lim\limits_{ x \rightarrow 0 } \frac{ \sqrt{1 + \text{sen } x} - \sqrt{1 - \text{sen } x} } {\tan x} \]
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\[ \lim\limits_{ \theta \rightarrow a } \frac{ \text{sen } \theta - \text{sen } a }{ \text{sen } \left( \frac{\theta}{2} \right) - \text{sen } \left( \frac{a}{2} \right) } \]
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\[ \lim\limits_{ x \rightarrow 0 } \frac{ \cos (a + x) - \cos (a - x) }{x} \]
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\[ \lim\limits_{ x \rightarrow 0 } \frac{ \text{sen } (a + x) - \text{sen } (a - x) }{ \tan (a + x) - \tan (a - x) } \]
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\[ \lim\limits_{ x \rightarrow \pi/6 } \frac{ 2 \text{ sen }^2 x - 3 \text{ sen } x + 1 }{ 2 \text{ sen }^2 x + \text{ sen } x - 1 } \]
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\[ \lim\limits_{ x \rightarrow \pi/4 } \frac{ 2 \tan^2 x - \tan x - 1 }{ 2 \tan^2 x - 3 \tan x + 1 } \]
Ver Respuestas
Respuestas
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\[ -1 \]
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\[ \frac{2}{3} \]
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\[ \frac{1}{2} \]
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\[ 0 \]
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\[ 0 \]
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\[ 0 \]
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\[ 1 \]
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\[ \frac{1}{2} \]
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\[ \frac{1}{2} \]
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\[ -\frac{\sqrt{3}}{3} \]
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\[ \frac{\sqrt{2}}{2} \]
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\[ \frac{\sqrt{2}}{8} \]
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\[ \pi \]
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\[ \frac{3}{4} \]
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\[ \frac{1}{2} \]
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\[ 0 \]
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\[ 1 \]
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\[ \frac{ 2 \cos a }{ \cos \left( \frac{a}{2} \right) } \]
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\[ -2\text{ sen } a \]
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\[ \cos^3 a \]
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\[ -\frac{1}{3} \]
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\[ 3 \]