# What is the limit of #(1 + 2/x)^x# as x approaches infinity?

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Jim, awesome ..

What this limit really represents is essentially the horizontal asymptote y =

Here are a couple of TI screenshots showing the graph and the decimal expansion for

But in fact you are looking at the curve endowed with concavity, not a straight line. The curve is asymptotically approaching the value of

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The limit of (1 + 2/x)^x as x approaches infinity is e^2.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you find the limit of #(((2+x)^3) -8 )/ x# as x approaches 0?
- How do you evaluate the limit #sqrt(x-1)/(x-4)# as x approaches #3#?
- What is the limit as x approaches 0 of #sin^2(x) 4x#?
- How do you find the x values at which #f(x)=3x-cosx# is not continuous, which of the discontinuities are removable?
- How do you find the limit of #(sin (2x)) / (sin (3x)) # as x approaches 0?

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