Manipulating limits

Mar 2013
56
0
Hallo!

I need some help.

lim x->4 ((2x^3-128)/(sqrt(x)-2))

i have tried manipulating the equation with conjugates but i just keep getting nowhere. wolfram has the limit at 384

please help!
 

zaidalyafey

Math Team
Aug 2012
1,177
44
Sana'a , Yemen
\(\displaystyle \lim_{x\to 4} \frac{2x^3\,-\,128}{sqrt {x}-2} \, \times \,\frac{sqrt {x}\,+\,2}{sqrt {x}\,+\,2}\)

\(\displaystyle \lim_{x\to 4} \frac{2(x^3\,-\,64)(\sqrt{x}\,+\,2)}{x\,-\,4}\)

\(\displaystyle \lim_{x\to 4} \frac{2(x\,-\,4)(x^2\,+4x\,+16)(\sqrt{x}\,+\,2)}{x\,-\,4}\)

\(\displaystyle \lim_{x\to 4} 2(x^2\,+4x\,+16)(\sqrt{x}\,+\,2)}= 2(16\,+\,16\,+16)(2\,+\,2)=48 \, \times\, 8=384\)