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AkiAncorD
@AkiAncorD
April 2021
1
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Lim x-3
x→3 √x+1 -2
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oganesbagoyan
Verified answer
Task/25824416
--------------------
Lim (x -3)/ (√(x+1) - 2)
x→3
* * * неопределенность типа 0/0 : (3 -3)
/
(√(3+1) - 2 )= 0
/
(√4 - 2 ) =0/0 * * *
Lim (x -3)/ (√(x+1) - 2) =Lim (x -3)
(√(x+1) + 2) /
(√(x+1) - 2)
(√(x+1) + 2)
=
x→3 x→3
Lim
(x -3)
(√(x+1) + 2)
/ (x -3)
=Lim
(√(x+1) + 2) =√(3+1) + 2 =4.
x→3 x→3
ответ : 4.
------- P.S. -------
(a-b)(a+b) =a² - b²
(√(x+1) - 2)(√(x+1) + 2) =(√(x+1) )² - 2² = x+1 -4 = x-3.
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Answers & Comments
Verified answer
Task/25824416--------------------
Lim (x -3)/ (√(x+1) - 2)
x→3
* * * неопределенность типа 0/0 : (3 -3)/(√(3+1) - 2 )= 0 /(√4 - 2 ) =0/0 * * *
Lim (x -3)/ (√(x+1) - 2) =Lim (x -3)(√(x+1) + 2) / (√(x+1) - 2)(√(x+1) + 2) =
x→3 x→3
Lim (x -3)(√(x+1) + 2) / (x -3) =Lim (√(x+1) + 2) =√(3+1) + 2 =4.
x→3 x→3
ответ : 4.
------- P.S. -------
(a-b)(a+b) =a² - b²
(√(x+1) - 2)(√(x+1) + 2) =(√(x+1) )² - 2² = x+1 -4 = x-3.