Question: Find the following limits if the limit is a finite number, \(\infty\), or \(-\infty\). Otherwise, show the limit does not exist. ( 7 points each)

1. \(\lim _{x \rightarrow 2} x^{2} \sqrt{3 x+1}\)
2. \(\lim _{x \rightarrow 3^{-}} \frac{2-x}{3-x}\)
3. \(\lim _{x \rightarrow 0^{-}} \frac{3 x-|x|}{x}\)
4. \(\underset{x\to 0}{\mathop{\lim }}\,\frac{3x-|x|}{x}\)
5. \(\lim _{x \rightarrow \infty} \sqrt{x^{2}+7 x}-x\)
6. \(\lim _{x \rightarrow 2} \frac{\frac{1}{x}-\frac{1}{2}}{x^{2}-2 x}\)

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