The graphs of
$\qquad f(x)=2\sqrt{x+1}-1\,,~~~~~ g(x)=\dfrac{x^2+x}{x}\,,~~~~$ and $~~~~ h(x)=e^x$
are shown below.
Select and drag cards to create a compound inequality that orders the values of $f(x)$, $g(x)$, and $h(x)$ for $x$ values near $0$, but not at $0$ itself. (A card may be used multiple times or not at all.)
[[☃ orderer 1]]
It follows that
[[☃ orderer 2]]
This means that
[[☃ orderer 3]]
Finally, the value of $\displaystyle ~\lim_{x \to 0} ~\dfrac{x^2+x}{x}~=~$ [[☃ math-keypad 1]].