Determine whether or not these two series converge: $$(A)\ \ \sum_{n=1}^{\infty}\sin\left(\frac{\cos{n}}{n^2}\right)\qquad (B)\ \  \sum_{n=1}^{\infty}\cos\left(\frac{\sin{n}}{n^2}\right)$$

The equation $x^y=y^x$ describes a curve in the first quadrant of the plane containing the point $P=(4, 2)$. Compute the slope of the line that is tangent to this curve at $P$.