\(\displaystyle \lim_{h \to 0} \theta\)

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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