왜 lim_ (x-> oo) (sqrt (4x ^ 2 + x-1) -sqrt (x ^ 2-7x + 3)) = lim_ (x-> oo) (3x ^ 2 + 8x-4) / 2x + ... + x + ...) = oo?

대답:

# "설명보기"#

# "곱하기"#

(sqrt (4 x ^ 2 + x - 1) + sqrt (x ^ 2 - 7 x + 3)) / + 3)) #

# "그럼 너는"#

(3x ^ 2 + 8x - 4) / (sqrt (4x ^ 2 + x - 1) + sqrt (x ^ 2 - 7x + 3)) #lim_ {x-

# "("(a-b) (a + b) = a ^ 2-b ^ 2 ")"#

(3x ^ 2 + 8x-4) / (sqrt (4x ^ 2) (1 + 1 / (4x) -1 / (4x2))) + sqrt (x ^ 2 (1-7 / x + 3 / x ^ 2)) #

(3x ^ 2 + 8x-4) / (2x sqrt (1 + 0-0) + x sqrt (1-0 + 0)) # = lim {x-

# "("lim_ {x-> oo} 1 / x = 0 "이기 때문에)"#

# = lim {x-> oo} (3 x ^ 2 + 8 x - 4) / (3 x) #

# = lim {x-> oo} (x + (8/3) - (4/3) / x) #

# = oo + 8/3 - 0 #

# = oo #