# How do you find lim (x+1)^(3/2)-x^(3/2) as x->1^+?

$2 \sqrt{2} - 1$
${\lim}_{x \to {1}^{+}} {\left(x + 1\right)}^{\frac{3}{2}} - {x}^{\frac{3}{2}}$
The function is continuous through x = 1 so you can just plug in the value x = 1 to get ${2}^{\frac{3}{2}} - 1 = \sqrt{8} - 1$