Let $\mathbb{R}$ be the set of all real numbers and $f: \mathbb{R} \rightarrow \mathbb{R}$ be a differentiable function satisfying $f^{\prime}(x)=x+f(x)$. If the graph of $f(x)$ passes through the origin then $\lim _{x \rightarrow 0} \frac{f(x)}{x^2}$

• A

  does not exist.
• B

  is equal to 0 .
• Correct answer
  C

  is equal to $1 / 2$.
• D

  is equal to 1 .

Hence, the correct answer is option: 'C'.