Question: Determine the limit of the function, if it exists:

1. \(\underset{x\to {{5}^{+}}}{\mathop{\lim }}\,\left( \frac{-3}{x-5} \right)\)
2. \(\underset{x\to 4}{\mathop{\lim }}\,\left( \frac{2-\sqrt{x}}{4-x} \right)\)
3. \(\underset{x\to -\infty }{\mathop{\lim }}\,\left( \frac{6{{x}^{3}}+4{{x}^{2}}-7}{15-7{{x}^{3}}} \right)\)
4. \(\underset{x\to -{{1}^{+}}}{\mathop{\lim }}\,f\left( x \right)\), where \(f\left( x \right)=\left\{ \begin{aligned} & 4{{x}^{3}}+5,\,\,\,\,x<-1 \\ & \sqrt{2x+11},\,\,x\ge -1 \\ \end{aligned} \right.\)
5. \(\underset{x\to \infty }{\mathop{\lim }}\,x{{e}^{-x}}\)

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