5. (10%) Let the function $f(t) = \sin(t^2)$ as shown in Figure 2. Consider two areas $A(x)$ and $B(x)$ for $x < 1.5$, where $A(x)$ represents the triangular area, while $B(x)$ designates the definite integral of $f(t)$ from $t = 0$ to $t = x$. Find

$$\lim_{x \to 0^+} \frac{A(x)}{B(x)}$$