I'm having trouble with limits that involve 0(adsbygoogle = window.adsbygoogle || []).push({}); ^{+}and 0^{-}. Can someone show me how the answers to the following limits are obtained?

[tex]f(x) = \frac{1}{1+e^{\frac{1}{x}}}[/tex]

[tex]\lim_{x\rightarrow0^{+}} = 0[/tex]

[tex]\lim_{x\rightarrow0^{-}} = 1[/tex]

Now, my second query involves continuity. I understand that:

[tex]f(x) \in C \Leftrightarrow \lim_{x \rightarrow a} f(x) = f(a)[/tex]

Say we have:

[tex]f(x) = \frac{\sin x}{x}[/tex]

Is f(x) continuous at x=0? My book says it is if f(0) is defined as 1. What am I missing?

Finally, what exactly is C^{n}?

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# Limits & Continuity

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