Let f : (0, infty) to (2, 20) be a twice diff | vedclass

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(C) Given that $\lim_{x 	o \infty} (f(x) + f'(x) + f''(x)) = 5$. Let $L = \lim_{x 	o \infty} f(x)$. Since $f(x)$ is bounded in $(2, 20)$,the limit e

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(C) Given that $\lim_{x 	o \infty} (f(x) + f'(x) + f''(x)) = 5$. Let $L = \lim_{x 	o \infty} f(x)$. Since $f(x)$ is bounded in $(2, 20)$,the limit exists. Consider the differential equation $f''(x) + f'(x) + f(x) = g(x)$. As $x 	o \infty$,$g(x) 	o 5$. For the linear differential equation with constant coefficients,the particular solution for the constant term $5$ is $f(x) = c$. Substituting $f(x) = c$ into the equation,we get $0 + 0 + c = 5$,so $c = 5$. Thus,$\lim_{x 	o \infty} f(x) = 5$. Since $\lim_{x 	o \infty} g(x) = 5$,we have $\lim_{x 	o \infty} (f(x) - g(x)) = 5 - 5 = 0$.

Let $f : (0, \infty) \to (2, 20)$ be a twice differentiable function such that $\lim_{x \to \infty} (f(x) + f'(x) + f''(x)) = \lim_{x \to \infty} g(x)$,where $\lim_{x \to \infty} g(x)$ exists and is equal to $5$. Then $\lim_{x \to \infty} (f(x) - g(x))$ is equal to:

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