Question: Find the following limits if they exist.

(a) \(\underset{x\to -4}{\mathop{\lim }}\,{{\left( x+2 \right)}^{3}}\)

(b) \(\underset{x\to 2}{\mathop{\lim }}\,{{x}^{2}}\sqrt{{{x}^{2}}+5x+2}\)

(c) \(\underset{x\to 6}{\mathop{\lim }}\,\frac{{{x}^{2}}-6x}{{{x}^{2}}-7x+6}\)

(d) \(\underset{t\to {{1}^{+}}}{\mathop{\lim }}\,\frac{3t}{\sqrt{t-1}}\)

(e) \[\underset{x\to {{0}^{+}}}{\mathop{\lim }}\,\frac{{{x}^{3}}-64x}{\sqrt[3]{{{x}^{2}}+2x}}\]

(f) \(\underset{x\to 1}{\mathop{\lim }}\,\frac{\sqrt{x}-1}{x-1}\)

(g) \(\underset{x\to 5}{\mathop{\lim }}\,\frac{\sqrt{x+4}-3}{x-5}\)

(h) \(\underset{x\to 2}{\mathop{\lim }}\,\frac{10}{{{x}^{2}}-4}\)

(i) \(\underset{x\to \infty }{\mathop{\lim }}\,\frac{{{x}^{2}}}{1+\frac{1}{{{x}^{2}}}}\)

(j) \(\underset{x\to +\infty }{\mathop{\lim }}\,\frac{4x+1}{\sqrt{{{x}^{2}}+1}}\)

(k) \(\underset{x\to -\infty }{\mathop{\lim }}\,\frac{2x+1}{3{{x}^{2}}+1}\)

(l) \(\underset{x\to +\infty }{\mathop{\lim }}\,\left( x-\sqrt{{{x}^{2}}+1} \right)\)

(m) \(\underset{x\to -\infty }{\mathop{\lim }}\,\frac{|x-5|}{x-5}\)

(n) \(\underset{x\to 1}{\mathop{\lim }}\,\frac{4-\sqrt{x+15}}{{{x}^{2}}-1}\)