\(\mathop {\lim }\limits_{x \to 0} \frac{{1 - {{\cos }^3}x}}{{x.\sin x}}\)
A.\(1\)
B.\(\frac{3}{2}\)
C.\(\frac{2}{3}\)
D.\(\frac{1}{2}\)

\(\mathop {\lim }\limits_{x \to 0} \frac{{\cos ax - \cos bx}}{{{x^2}}}\)
A.\(\frac{a^{2} - b^{2}}{2}\)
B.\(\frac{a^{2} + b^{2}}{2}\)
C.\( a^{2} - b^{2}\)
D.\(\frac{b^{2} - a^{2}}{2}\)

\(\mathop {\lim }\limits_{x \to 0} \frac{{\sin 6x + \sin 4x}}{{\sin 3x + \sin 5x}}\)
A.\(1\)
B.\(\frac{4}{3}\)
C.\(\frac{1}{2}\)
D.\(\frac{5}{4}\)

\(\mathop {\lim }\limits_{x \to 0} \frac{{1 - \sin 2x - \cos 2x}}{{1 - \sin 2x + \cos 2x}}\)
A.\(1\)
B.\( - 1\)
C.\(0\)
D.\(\frac{1}{2}\)

\(\mathop {\lim }\limits_{x \to a} \frac{{{{\sin }^2}x - {{\sin }^2}a}}{{{x^2} - {a^2}}}\)
A.\(\frac{\sin {a}}{a}\)
B.\(\frac{\sin {2a}}{2a}\)
C.\(\frac{\cos {a}}{a}\)
D.\(\frac{\cos {2a}}{2a}\)

\(\mathop {\lim }\limits_{x \to \frac{\pi }{4}} \frac{{\sin \left( {\frac{\pi }{4} - x} \right)}}{{1 - \sqrt 2 \sin x}}\)
A.\(1\)
B.\(\frac{1}{2}\)
C.\(2\)
D.\( - 1\)

\(\mathop {\lim }\limits_{x \to \frac{\pi }{6}} \frac{{2\sin x - 1}}{{4{{\cos }^2}x - 3}}\)
A.\( - \frac{3}{2}\)
B.\( - \frac{1}{4}\)
C.\(\frac{1}{2}\)
D.\( - \frac{1}{2}\)

\(\mathop {\lim }\limits_{x \to \frac{\pi }{6}} \frac{{2\sin x - 1}}{{4{{\cos }^2}x - 3}}\)
A.\( - \frac{3}{2}\)
B.\( - \frac{1}{4}\)
C.\(\frac{1}{2}\)
D.\( - \frac{1}{2}\)

\(\mathop {\lim }\limits_{x \to b} \frac{{\cos x - \cos b}}{{x - b}}\)
A.\(\sin b\)
B.\( - \cos b\)
C.\( - \sin b\)
D.\(\cos b\)

\(\mathop {\lim }\limits_{x \to a} \frac{{{{\sin }^2}x - {{\sin }^2}a}}{{{x^2} - {a^2}}}\)
A.\(\frac{\sin {a}}{a}\)
B.\(\frac{\sin {2a}}{2a}\)
C.\(\frac{\cos {a}}{a}\)
D.\(\frac{\cos {2a}}{2a}\)