Calculating Limit of Function – A quotient of polynomials to the power of a quotient – Exercise 5996

Exercise

Evaluate the following limit:

limx(1+x2+x)1x1x\lim _ { x \rightarrow \infty} {(\frac{1+x}{2+x})}^{\frac{1-\sqrt{x}}{1-x}}

Final Answer


limx(1+x2+x)1x1x=1\lim _ { x \rightarrow \infty} {(\frac{1+x}{2+x})}^{\frac{1-\sqrt{x}}{1-x}}=1

Solution

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