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(A) Given the integral equation: $f(x) = \int_0^x f(t) \, dt$. By the Fundamental Theorem of Calculus,differentiating both sides with respect to $x$ g

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(A) Given the integral equation: $f(x) = \int_0^x f(t) \, dt$. By the Fundamental Theorem of Calculus,differentiating both sides with respect to $x$ gives: $f'(x) = f(x)$. This is a first-order linear differential equation: $\frac{dy}{dx} = y$. Separating the variables,we get: $\int \frac{dy}{y} = \int dx$. Integrating both sides: $\ln |y| = x + C$,which implies $y = Ae^x$. From the given equation,$f(0) = \int_0^0 f(t) \, dt = 0$. Substituting $x = 0$ and $y = 0$ into $y = Ae^x$,we get $0 = Ae^0$,which implies $A = 0$. Therefore,$f(x) = 0$ for all $x \in \mathbb{R}$. Thus,$f(\ln 5) = 0$.

Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a continuous function which satisfies $f(x) = \int_0^x f(t) \, dt$. Then the value of $f(\ln 5)$ is

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