Question

lim y->2 (sqrt(y+2)-2)/(y-2)

Answer 1

lim (√(y+2) - 2)/(y-2) as y ---> 2

= lim (√(y+2) - 2)/(y-2)*(√(y+2) + 2)/(√(y+2) + 2)
= lim (y+2 - 4)/((y+2)((√(y+2) + 2))
= lim 1/((√(y+2) + 2)) , as y --> 2
= 1/(√4 + 2)
= 1/4