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If lim(trarrx)(e^(t)f(x)-e^(x)f(t))/((t-...

If `lim_(trarrx)(e^(t)f(x)-e^(x)f(t))/((t-x)(f(x))^(2))=2 andf(0)=(1)/(2),` then find the value of `f'(0).`

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4

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2

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0

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1

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To solve the problem, we need to find the value of \( f'(0) \) given the limit: \[ \lim_{t \to x} \frac{e^t f(x) - e^x f(t)}{(t - x)(f(x))^2} = 2 \] and the condition \( f(0) = \frac{1}{2} \). ...
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