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If lim(xtoa)[f(x)+g(x)]=2 and lim(xtoa) ...

If `lim_(xtoa)[f(x)+g(x)]=2` and `lim_(xtoa) [f(x)-g(x)]=1,` then find the value of `lim_(xtoa) f(x)g(x).`

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To solve the problem, we need to find the value of \( \lim_{x \to a} f(x)g(x) \) given the limits \( \lim_{x \to a} [f(x) + g(x)] = 2 \) and \( \lim_{x \to a} [f(x) - g(x)] = 1 \). ### Step-by-Step Solution: 1. **Define Limits**: Let: \[ \lim_{x \to a} f(x) = A \quad \text{and} \quad \lim_{x \to a} g(x) = B ...
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