Question: Find the following limits if they exist.

1. \(\underset{x\to -4}{\mathop{\lim }}\,{{\left( x+2 \right)}^{3}}\)
2. \(\underset{x\to 2}{\mathop{\lim }}\,{{x}^{2}}\sqrt{{{x}^{2}}+5x+2}\)
3. \(\underset{x\to 6}{\mathop{\lim }}\,\frac{{{x}^{2}}-6x}{{{x}^{2}}-7x+6}\)
4. \(\underset{t\to {{1}^{+}}}{\mathop{\lim }}\,\frac{3t}{\sqrt{t-1}}\)
5. \[\underset{x\to {{0}^{+}}}{\mathop{\lim }}\,\frac{{{x}^{3}}-64x}{\sqrt[3]{{{x}^{2}}+2x}}\]
6. \(\underset{x\to 1}{\mathop{\lim }}\,\frac{\sqrt{x}-1}{x-1}\)
7. \(\underset{x\to 5}{\mathop{\lim }}\,\frac{\sqrt{x+4}-3}{x-5}\)
8. \(\underset{x\to 2}{\mathop{\lim }}\,\frac{10}{{{x}^{2}}-4}\)
9. \(\underset{x\to \infty }{\mathop{\lim }}\,\frac{{{x}^{2}}}{1+\frac{1}{{{x}^{2}}}}\)
10. \(\underset{x\to +\infty }{\mathop{\lim }}\,\frac{4x+1}{\sqrt{{{x}^{2}}+1}}\)
11. \(\underset{x\to -\infty }{\mathop{\lim }}\,\frac{2x+1}{3{{x}^{2}}+1}\)
12. \(\underset{x\to +\infty }{\mathop{\lim }}\,\left( x-\sqrt{{{x}^{2}}+1} \right)\)
13. \(\underset{x\to -\infty }{\mathop{\lim }}\,\frac{|x-5|}{x-5}\)
14. \(\underset{x\to 1}{\mathop{\lim }}\,\frac{4-\sqrt{x+15}}{{{x}^{2}}-1}\)

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