Limit of a function approaching infinity with 2 constants. $$\lim_{x \to +∞}{\sqrt{x^2 + bx + c} - x}.$$
What is the limit of this function as it approaches infinity?
So in this limit, I tried inputting several values in the equation since it is approaching infinity, and I seem to get √bx + √c.
However, I don't think this is telling me anything. Am I reading the question from the wrong perspective?
Thanks

\begin{align*}
\lim_{x\rightarrow +\infty}\left(\sqrt{x^2+bx+c}-x \right)&=\lim_{x\rightarrow +\infty}\frac{bx+c}{\sqrt{x^2+bx+c}+x }\\
&=\lim_{x\rightarrow +\infty}\frac{b+\frac{c}{x}}{\sqrt{1+\frac{b}{x}+\frac{c}{x^2}}+1 }\\
&=\frac{b}{2}.
\end{align*}
