Question
Plot the function $y=\left(1+\frac{1}{x}\right)^{x} .$ What is the horizontal asymptote as $x$ increases?
Step 1
We can use the fact that $e^x$ is the limit of $\left(1+\frac{x}{n}\right)^n$ as $n$ approaches infinity. So, we can rewrite the function as $y=e^{(\ln(1+\frac{1}{x}))x}$. Show more…
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