> 
> Find all possible values of the triple $(a, b, c)$ of constants for which the limit 
>  $$\displaystyle \lim\_{x\to0^+} \frac{\arctan\left(x+\frac{a}{x}\right)+bx+c}{x^5}$$ 
>  exists and find the limit for each of these values of $(a, b, c)$.
> 
> 
> 

So, I’ve been trying to solve this problem by using L’Hospital’s Rule over and over but it doesn’t lead me anywhere? What should I do? Can somebody lead me?