A calculus problem by Sambhrant Sachan

Calculus Level 4

\[ \large \lim_{x\to0} \dfrac{x(1+a\cos{x})-b\sin{x}}{x^3}= 1 \]

Let \(a\) and \(b\) be constants satisfying the equation above. Find \(\lfloor a^4 \times b^4 \rfloor\).

Notations: \( \lfloor \cdot \rfloor \) denotes the floor function.

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