Question

$\underset{x\to 4}{\lim }\left[\frac{x^{3/2}-8}{x-4}\right]$ equals

• A. 3
• B. 1
• C. 2
• D. $\frac{2}{3}$
• E. $\frac{3}{2}$

Answer 1

Answer: (A)

$y=\underset{x\to 4}{\lim }\left[\frac{x^{3/2}-8}{x-4}\right]=\underset{x\to 4}{\lim }\left[\frac{{\left(x^{1/2}\right)}^3-(2{)}^3}{(\sqrt{x}-2)(\sqrt{x}+2)}\right]$
$y=\underset{x\to 4}{\lim }\left[\frac{\left(x^{1/2}-2\right)(x+4+2\sqrt{x})}{(\sqrt{x}-2)(\sqrt{x}+2)}\right]$
$y=\underset{x\to 4}{\lim }\frac{(x+4+2\sqrt{x})}{(\sqrt{x}+2)}=\frac{12}{4}=3$