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\[\lim_{x \to 0} \frac{\sqrt{1 + \sin x} - \sqrt{1 - \sin x}}{x}\]
Concept: undefined >> undefined
\[\lim_{x \to 0} \frac{1 - \cos 4x}{x^2}\]
Concept: undefined >> undefined
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\[\lim_{x \to 0} \frac{x \cos x + \sin x}{x^2 + \tan x}\]
Concept: undefined >> undefined
\[\lim_{x \to 0} \frac{1 - \cos 2x}{3 \tan^2 x}\]
Concept: undefined >> undefined
\[\lim_\theta \to 0 \frac{1 - \cos 4\theta}{1 - \cos 6\theta}\]
Concept: undefined >> undefined
\[\lim_{x \to 0} \frac{ax + x \cos x}{b \sin x}\]
Concept: undefined >> undefined
\[\lim_\theta \to 0 \frac{\sin 4\theta}{\tan 3\theta}\]
Concept: undefined >> undefined
Evaluate the following limits:
\[\lim_{x \to 0} \frac{2\sin x - \sin2x}{x^3}\]
Concept: undefined >> undefined
\[\lim_{x \to 0} \frac{1 - \cos 5x}{1 - \cos 6x}\]
Concept: undefined >> undefined
\[\lim_{x \to 0} \frac{cosec x - \cot x}{x}\]
Concept: undefined >> undefined
\[\lim_{x \to 0} \frac{\sin 3x + 7x}{4x + \sin 2x}\]
Concept: undefined >> undefined
\[\lim_{x \to 0} \frac{5x + 4 \sin 3x}{4 \sin 2x + 7x}\]
Concept: undefined >> undefined
\[\lim_{x \to 0} \frac{3 \sin x - \sin 3x}{x^3}\]
Concept: undefined >> undefined
\[\lim_{x \to 0} \frac{\tan 2x - \sin 2x}{x^3}\]
Concept: undefined >> undefined
\[\lim_{x \to 0} \frac{\sin ax + bx}{ax + \sin bx}\]
Concept: undefined >> undefined
\[\lim_{x \to 0} \left( cosec x - \cot x \right)\]
Concept: undefined >> undefined
Evaluate the following limit:
\[\lim_{x \to 0} \frac{\sin\left( \alpha + \beta \right)x + \sin\left( \alpha - \beta \right)x + \sin2\alpha x}{\cos^2 \beta x - \cos^2 \alpha x}\]
Concept: undefined >> undefined
Evaluate the following limits:
\[\lim_{x \to 0} \frac{\cos ax - \cos bx}{\cos cx - 1}\]
Concept: undefined >> undefined
Evaluate the following limit:
\[\lim_{h \to 0} \frac{\left( a + h \right)^2 \sin\left( a + h \right) - a^2 \sin a}{h}\]
Concept: undefined >> undefined
If \[\lim_{x \to 0} kx cosec x = \lim_{x \to 0} x cosec kx,\]
Concept: undefined >> undefined
