Made ANOTHER FKING mistake *** NEW Basic calculus limit question FML save me will rate quickly? sorry philo

m really sorry i made a mistake

i made another ******* mistake denominator is y squared -1

lim y-->1 (y-(4sqrt(y)) +3) / (y^2-1)

thanks for your patience guys sorry its late and im going nuts

There are at least two methods.

Method 1 (simplifying by factoring top and bottom):

lim y-->1 (y-(4sqrt(y)) +3) / (y^2-1)
= lim y-->1 ((sqrt(y))^2 - (4sqrt(y)) +3) / (y^2-1)
= lim y-->1 (sqrt(y) - 1)(sqrt(y) - 3) / [(y - 1)(y + 1)]
= lim y-->1 (sqrt(y) - 1)(sqrt(y) - 3) / [((sqrt(y))^2 - 1)(y + 1)]
= lim y-->1 (sqrt(y) - 1)(sqrt(y) - 3) / [(sqrt(y) - 1)(sqrt(y) + 1)(y + 1)]
= lim y-->1 (sqrt(y) - 3) / [(sqrt(y) + 1)(y + 1)]
= (sqrt(1) - 3) / [(sqrt(1) + 1)(1 + 1)]
= -2/[(2)(2)]
= -1/2

Method 2 (L'Hopital's rule on the indeterminate from 0/0):

lim y-->1 (y-(4sqrt(y)) +3) / (y^2-1)
= lim y-->1 (d/dy)(y-(4sqrt(y)) +3) / (d/dy)(y^2-1)
= lim y-->1 (1 - 2/sqrt(y)) / (2y)
= (1 - 2/sqrt(1)) / (2*1)
= -1/2.

Lord bless you today!