# Limit at $$0^+$$

Calculus Level pending

Consider the function $$f(x)=\frac{1}{x}$$. For each positive value of $$h$$, define $$\theta_h$$ to be the unique positive value that satisfies the equation $f( 2 + h) = f(2) + h f'(2 + \theta_h h ).$ What is the value of $$\displaystyle \lim_{h \to 0^+} \frac{1}{\theta_h}$$?

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