Question

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

Answer 1

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

Answer 2

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

Answer 3

Simplify that.

Answer 4

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

Answer 5

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

Answer 6

No worries.