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OpenStudy (anonymous):

I need help calculating a limit without using approximation or graphical methods, the equation is as follows:

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OpenStudy (anonymous):

\[\lim_{x \rightarrow 0} \frac{ \frac{ 1 }{ x-2 }+\frac{ 1 }{ 2 } }{ x }\]

OpenStudy (anonymous):

\[\huge \lim_{x \rightarrow 0}\frac{\frac{1}{x-2}+\frac{1}{2}}{x}=\lim_{x \rightarrow 0}\frac{\frac{2+x-2}{2(x-2)}}{x}\] \[\huge =\lim_{x \rightarrow 0}\frac{x}{2(x-2)}\times \frac{1}{x}\]

OpenStudy (anonymous):

Simplify that.

OpenStudy (anonymous):

and then sub in x=0 to find your limit.

OpenStudy (anonymous):

@Azteck Thank you! I got -1/4 :)

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OpenStudy (anonymous):

No worries.

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