Calculating Limit of Function – A quotient of polynomials to the power of a quotient of functions – Exercise 5941

Exercise

Evaluate the following limit:

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

$$\lim _ { x \rightarrow 1} {(\frac {1+x} {2+x})}^{\frac{1-\sqrt{x}}{1-x}}=\sqrt{\frac {2} {3}}$$