대답:
(sqrt (1 + x ^ 2) -sqrt (1 + x)) / (sqrt (1 + x ^ 3) -sqrt (1 + x)) = 1 #
설명:
L' Hopital의 규칙을 사용하면 = (f '(a)) / (g'(a)) #lim_ (x-> a) (f (x)) /
#f (x) = sqrt (1 + x ^ 2) -sqrt (1 + x) #
# = (1 + x ^ 2) ^ (1/2) - (1 + x) ^ (1/2) #
(1 + x) ^ (- 1/2) / 2 # (2)
# g (x) = sqrt (1 + x ^ 3) -sqrt (1 + x) #
# = (1 + x ^ 3) ^ (1/2) - (1 + x) ^ (1/2) #
(1 + x) ^ (- 1 / 2) / 2 # (2)
(1 + x)) = (0 (1 + x)) = ((0 + 1) (1 + 0 ^ 3) ^ (- 1/2) - (1 + 0) ^ (1/2)) / 2- (1 + 0) ^ (- 1/2) / 2) #
#=(-(1+0)^(-1/2)/2)/(-(1+0)^(-1/2)/2)#
# - 취소 (- (1 + 0) ^ (- 1/2) / 2) / 취소 (- (1 + 0) ^ (- 1/2) / 2) = 1 #
