Calculating Limit of Function – A quotient of polynomials to the power of a polynomial – Exercise 6012

Exercise

Evaluate the following limit:

$$\lim _ { x \rightarrow \infty} {(\frac{x-3}{x-2})}^{2x+4}$$

$$\lim _ { x \rightarrow \infty} {(\frac{x-3}{x-2})}^{2x+4}=e^{-2}$$