# Take it to the limit

Calculus Level 3

Given $$f\left( x \right) = \frac{x + 5}{2}$$, $$g\left( x \right) = x + 7$$, $$\lim_{x \rightarrow 6}{f\left( g\left( x \right)\right)} = L$$ and that $$\lvert f\left( g\left( x \right)\right) - L \rvert < 0.005$$, what is the value of $$\delta$$ such that $$\lvert x - 6 \rvert < \delta$$?

Detail: all the functions' domains and codomains, in this problem, are the set of the Real Numbers.

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