Understanding Exponential Decay: Exploring the Behavior of e^x as x Approaches Negative Infinity

e^x, när x -> -∞

When we take the limit of a function as x approaches negative infinity, we evaluate what happens to the function as x gets smaller and smaller

When we take the limit of a function as x approaches negative infinity, we evaluate what happens to the function as x gets smaller and smaller.

In this case, we are looking at the function e^x as x approaches negative infinity. The function e^x represents exponential growth, where the base of the function is the constant Euler’s number, e (approximately 2.71828).

As x approaches negative infinity, e^x will approach 0. This is because as x becomes more negative, the value of e^x will become closer and closer to 0, but never actually reach it.

To see why this happens, let’s consider a few values of x as they decrease towards negative infinity:
– If x = -1, then e^x = e^(-1) ≈ 0.368.
– If x = -10, then e^x = e^(-10) ≈ 0.0000454.
– If x = -100, then e^x = e^(-100) ≈ 3.72 x 10^(-44).
– If x = -1000, then e^x = e^(-1000) ≈ 0.

As you can see, as x becomes more negative, e^x becomes exponentially smaller and approaches 0.

To summarize, when x approaches negative infinity, the function e^x approaches 0.

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