# $$\displaystyle \lim_{h \to 0} \theta$$

Calculus Level 2

For function $$f(x)=x^3+9,$$ constant $$\theta$$ satisfies $f(x+h)-f(x)=hf'(x+\theta h),$ where $$x > 0$$, $$h > 0$$ and $$0 < \theta < 1.$$ What is the value of $$\displaystyle \lim_{h \to 0} \theta?$$

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