# 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.

×