Question

limit -> 2 xpower10 - 1024/x-2

Answer 1

Hey

$\lim_{x - > 2} \frac{ {x}^{10} - 1024 }{x - 2}$

$= \lim_{x - > 2} \frac{ (x - 2) \sum_{n = 0}^{9}( {2}^{n} {x}^{9 - n} ) }{x - 2}$

$=\lim_{x - > 2}( \sum_{n = 0}^{9}( {2}^{n} {x}^{9 - n} ))$

$= \sum_{n = 0}^{9}( {2}^{9} )$

$=5 ({2}^{10} )$
Or..

By L - Hospital :

( The limit has 0/0 form )

Differentiate the Numerator and Denominator to get :

$\lim_{x - > 2} \frac{ {x}^{10} - 1024 }{x - 2}$

$= \lim_{x - > 2} \frac{ 10 {x}^{9} }{1} = 10( {2}^{9} )$

$= 5( {2}^{10} )$
Both ways ! you get your answer ^^"