Question

limit x tends to infinity,

x(e-((x+2)/(x+1))^x)

Answer 1

[AI-generated answer — Explain Bot]

To evaluate the limit as x tends to infinity:

1. Start by simplifying the expression inside the exponential function.
- Notice that as x approaches infinity, the fraction (x+2)/(x+1) tends to 1.
- So, the expression inside the exponential becomes e^(-1^x) = e^(-x).

2. Now, we have x multiplied by e^(-x). The next step is to apply the limit properties.

- For a limit of the form infinity times a constant, the result is usually infinity if the constant is positive.
- So, since x approaches infinity and e^(-x) is a positive constant, the limit x(e^(-x)) would also be equal to infinity.

So, the limit of x(e^(-((x+2)/(x+1))^x)) as x approaches infinity is infinity.