Compute the limit lim_{x->0} (e^x - e^{-x})/(2x).

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Multiple Choice

Compute the limit lim_{x->0} (e^x - e^{-x})/(2x).

Explanation:
When x approaches 0, the top and bottom both approach 0, so you can use L'Hôpital's rule. Differentiate the numerator: the derivative of e^x is e^x and the derivative of -e^{-x} is +e^{-x}, giving e^x + e^{-x}. The derivative of the bottom is 2. Now evaluate at x = 0: (e^0 + e^0)/2 = (1 + 1)/2 = 1. Therefore, the limit is 1.

When x approaches 0, the top and bottom both approach 0, so you can use L'Hôpital's rule. Differentiate the numerator: the derivative of e^x is e^x and the derivative of -e^{-x} is +e^{-x}, giving e^x + e^{-x}. The derivative of the bottom is 2. Now evaluate at x = 0: (e^0 + e^0)/2 = (1 + 1)/2 = 1. Therefore, the limit is 1.

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