Question: Evaluate the following limits

(a) \(\underset{x\to 3}{\mathop{\lim }}\,{{\left( \frac{5x+1}{{{x}^{2}}-8} \right)}^{3/4}}\)

(b) \(\underset{x\to 5}{\mathop{\lim }}\,\frac{25-{{x}^{2}}}{{{x}^{2}}-10x+25}\)

(c) \[\underset{t\to -3}{\mathop{\lim }}\,\frac{\frac{1}{\sqrt{12+t}}-\frac{1}{3}}{t+3}\]

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

(e) \(\underset{\theta ->0}{\mathop{\lim }}\,\frac{1-\cos 2\theta }{3{{\theta }^{2}}}\)

(f) \(\underset{x\to -\infty }{\mathop{\lim }}\,\frac{1-{{e}^{x}}}{1+{{e}^{x}}}\)