## Thomas' Calculus 13th Edition

$-2$
We will calculate the limit for $\lim\limits_{(x,y) \to (\pi,\ln 2)} e^y \cos x$ This implies that $\lim\limits_{(x,y) \to (\pi,\ln 2)} e^y \cos x=e^{(\ln 2)} \cos (\pi)$ Thus, $\lim\limits_{(x,y) \to (\pi,\ln 2)} e^y \cos x=e^{(\ln 2)} \cos (\pi)=2 \times (-1)=-2$