Calculate \(\lim _{ x\rightarrow0}{|x| } \).

Consider the function f(x) = \(\sqrt{x},x\ge0.\) Does\(lim_{x\rightarrow0}f(x)\) exist?

Evaluate \(lim_{x\rightarrow 2^-}\left\lfloor x \right\rfloor \) and \(lim_{x\rightarrow 2^+}\left\lfloor x \right\rfloor \) .

In problems 1-6, using the table estimate the value of the limit.
\(lim_{x\rightarrow 2}{x-2\over x^2-x-2}\)

x	1.9	1.99	1.999	2.001	2.01	2.1
f(x)	0.344820	0.33444	0.33344	0.333222	0.33222	0.332258

In problem, using the table estimate the value of the limit
\(lim_{x\rightarrow 0}{sin x\over x}\)

x	-0.1	-0.01	-0.001	0.001	0.01	0.1
f(x)	0.99833	0.99998	0.99999	0.99999	0.99998	0.99833

In problem, using the table estimate the value of the limit
\(lim_{x\rightarrow0}{cos x-1\over x}\)

x	-0.1	-0.01	-0.001	0.001	0.01	0.1
f(x)	0.04995	0.0049999	0.0004999	–0.0004999	–0.004999	–0.04995

Use the graph to find the limits (if it exists). If the limit does not exist, explain why?
\(lim_{x\rightarrow{1}}sin \pi x\)

Use the graph to find the limits (if it exists). If the limit does not exist, explain why?
\(lim_{x \rightarrow{\pi\over 2}} tanx\)

If the limit of f(x) as x approaches 2 is 4, can you conclude anything about f(2)? Explain reasoning.

Calculate \(lim_{x\rightarrow3}(x^3-2x+6).\)