Chapter 6 - Inverse Functions - 6.2 Exponential Functions and Their Derivatives - 6.2 Exercises - Page 418: 27

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Need to find the limit for $\lim\limits_{x \to2^{+}}e^{\frac{3}{(2-x)}}$. Consider $y=\lim\limits_{x \to2^{+}}e^{\frac{3}{(2-x)}}$ when ${x \to 2^{+}}$ then $(2-x) \to 0^{-}$ Thus, $y=\lim\limits_{x \to2^{+}}e^{\frac{3}{(2-x)}}=-\infty$ We have found the fact that $\lim\limits_{x \to2^{+}}e^{\frac{3}{(2-x)}}=\lim\limits_{y \to-\infty}e^{\frac{3}{(2-x)}}=e^{-\infty}=\frac{1}{e^{\infty}}=0$