Вычислить предел:

lim

x→5

Lim ((x-5) / (2-√ (x-1)) = (5-5) / (2-√ (5-1)) = 0/0

x->5

lim ((x-5) / (2-√ (x-1)) = lim ((x-5) * (2+√ (x-1))) / ((2-√ (x-1)) * (2+√ (x-1)) =

x->5 x->5

lim ((x-5) * ((2-√ (x-1))) / (2² - (√ (x-1)) ²) = lim ((x-5) * (2+√ (x-1))) / (4-x+1)) =

x->5 x->5

lim ((x-5) * (2+√ (x-1)) / (x-5)) = lim (2+√x-1)) = 2+√ (5-1) = 2+2=4

x->5 x->5