Asked by rodrigo
lim y->2 (sqrt(y+2)-2)/(y-2)
Answers
Answered by
Reiny
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
= 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
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