Lim 2√х+3-4/х-1 (x+3 - под корнем, 2√х+3-4 - числитель, х-1 - знаменатель)

x->1

Lim ((2√ (x+3) - 4) / (x-1)) = (2*√ (1+3) - 4) / (1-1) = 0/0

x->1

lim ((2√ (x+3) - 4) / (x-1)) =

x->1

=lim ((2√ (x+3) - 4) * (2√ (x+3) + 4)) / ((x-1) * (2√ (x+3) + 4)) =

x->1

=lim ((2√ (x+3)) ²-4²) / ((x-1) * (2√ (x+3) + 4) =

x->1

=lim (4 * (x+3) - 16) / ((x-1) * (2√ (x+3) + 4)) =

x->1

=lim (4x-4) / ((x-1) * (2√ (x+3) + 4)) =

x->1

=lim (4 * (x-1)) / ((x-1) * (2 (√ (x+1) + 2)) =

x->1

=lim4/2 (√ (x+3) + 2) = lim2 / (√ (x+3) + 2) = 2 / (√ (1+3) + 2) = 2/4=1/2=0,5

x->1