Calculus
posted by Shayna on .
Explain how lim x>1 ((x^2)1)/(sqrt(2x+2)2) = 4

Rationalize the denominator, that is, multiply top and bottom by √(2x+2) + 2 to give you
lim [(x^2  1)/(√(2x+2)  2) ] * (√(2x+2) + 2)/(√(2x+2) + 2)
= (x+1)(x1)(√(2x+2) + 2)/(2x+2  4)
= (x+1)(x1)(√(2x+2) + 2)/( 2(x1))
= lim (x+1)(√(2x+2) + 2)/2 as x > 1
= 2(√4+2)/2 = 4 
=24