Задача 42318 ...

alenka5poi5

2019-12-06 06:11:39

limsqrt(3x-5)-4/2x-14
x → 7

sova

2019-12-06 08:30:12

★

lim_(x → 7)(√(3x–5)–4)/(2x–14)=0/0=

умножаем на (√(3x–5)+4) и числитель и знаменатель:

lim_(x → 7)(√(3x–5)–4)(√(3x–5)+4)/(2x–14)√(3x–5)+4)=

по формуле (a-b)(a+b)=a^2-b^2

lim_(x → 7)((√(3x–5))^2–4^2)/(2x–14)√(3x–5)+4)=


=lim_(x → 7)(3x–5–16)/(2x–14)√(3x–5)+4)=

cокращаем на (х-7):

lim_(x → 7)(3)/(2)*√(3x–5)+4)=3/(2*(sqrt(16)+4))=3/16