As x approaches 0, what is the limit of (e^x - 1)/x?

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Multiple Choice

As x approaches 0, what is the limit of (e^x - 1)/x?

Explanation:
The expression (e^x − 1)/x as x goes to 0 is the derivative of e^x at 0. Since the derivative of e^x is e^x, evaluating at x = 0 gives e^0 = 1. So the limit is 1. Another way to see it is with the Taylor expansion e^x = 1 + x + x^2/2 + ..., which makes (e^x − 1)/x = 1 + x/2 + x^2/6 + ..., and this tends to 1 as x approaches 0.

The expression (e^x − 1)/x as x goes to 0 is the derivative of e^x at 0. Since the derivative of e^x is e^x, evaluating at x = 0 gives e^0 = 1. So the limit is 1.

Another way to see it is with the Taylor expansion e^x = 1 + x + x^2/2 + ..., which makes (e^x − 1)/x = 1 + x/2 + x^2/6 + ..., and this tends to 1 as x approaches 0.

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