Question: Evaluate the following limits, justifying your answers. If a limit does not exist explain why

a- \(\underset{x\to \infty }{\mathop{\lim }}\,\frac{3{{x}^{3}}+\cos x}{\sin x-{{x}^{3}}}\)

b- \(\underset{x\to {{\pi }^{+}}}{\mathop{\lim }}\,\frac{\arctan \left( \frac{1}{x-\pi } \right)}{\pi -x}\)

c- \(\underset{x\to {{0}^{+}}}{\mathop{\lim }}\,\sqrt{x+\sin x\ln x}\)

d- \(\underset{x\to {{1}^{-}}}{\mathop{\lim }}\,\frac{\arccos x}{1-x}\)

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