iran-konkur 2020 Q129

iran-konkur · Other · konkur-riazi_1399_specialized_old-curriculum Second order differential equations Verifying a particular solution satisfies a second-order ODE
129. The function with the rule $f(x) = \displaystyle\lim_{n \to +\infty} \left(1 - \dfrac{3x}{n}\right)^n$ is defined for every real number $x$. Which statement is correct?
  • [(1)] $f''(x) + 6f'(x) + 9f(x) = 0$
  • [(2)] $f''(x) + 3f'(x) + 2f(x) = 0$
  • [(3)] $f''(x) - 6f'(x) + 9f(x) = 0$
  • [(4)] $f''(x) - 3f'(x) + 2f(x) = 0$
\textbf{129.} The function with the rule $f(x) = \displaystyle\lim_{n \to +\infty} \left(1 - \dfrac{3x}{n}\right)^n$ is defined for every real number $x$. Which statement is correct?

\begin{itemize}
    \item[(1)] $f''(x) + 6f'(x) + 9f(x) = 0$
    \item[(2)] $f''(x) + 3f'(x) + 2f(x) = 0$
    \item[(3)] $f''(x) - 6f'(x) + 9f(x) = 0$
    \item[(4)] $f''(x) - 3f'(x) + 2f(x) = 0$
\end{itemize}