Question: Evaluate following limits if exist(s)

a) \[{{\lim }_{x\to -4}}\frac{{{x}^{2}}+5x+4}{{{x}^{2}}+3x-4}\]

b) \[{{\lim }_{x\to {{2}^{+}}}}\frac{|x-2|}{x-2}\]

c) \[{{\lim }_{x\to -2}}\frac{{{x}^{3}}+8}{x+2}\]

d) \[{{\lim }_{x\to \infty }}2-{{x}^{-3}}\]

e) \[{{\lim }_{x\to 3}}\frac{x+3}{{{x}^{2}}-9}\]