Limit of Function – A function to the power of a function – Exercise 5384

Exercise

Evaluate the limit

$$\lim _ { x \rightarrow 2} {(\frac{x}{2})}^{\frac{1}{x-2}}$$

$$\lim _ { x \rightarrow 2} {(\frac{x}{2})}^{\frac{1}{x-2}}=\frac{1}{2}$$