Ano ang limitasyon ng function na ito bilang h papuntang 0? (h) / (sqrt (4 + h) -2)

#Lt_ (h-> o) (h) / (sqrt (4 + h) -2) #

# = Lt_ (h-> o) (h (sqrt (4 + h) +2)) / ((sqrt (4 + h) -2)

# = Lt_ (h-> o) (h (sqrt (4 + h) +2)) / (4 + h-4) #

# = Lt_ (h-> o) (cancelh (sqrt (4 + h) +2)) / cancelh "bilang" h! = 0 #

# = (sqrt (4 + 0) +2) = 2 + 2 = 4 #

Sagot:

# 4#.

Paliwanag:

Tandaan na, #lim_ (h hanggang 0) (f (a + h) -f (a)) / h = f '(a) ………… (ast) #.

Hayaan, #f (x) = sqrtx, "kaya na," f '(x) = 1 / (2sqrtx) #.

#:. f '(4) = 1 / (2sqrt4) = 1/4 #.

Ngunit, # f '(4) = lim_ (h hanggang 0) (sqrt (4 + h) -sqrt4) / h ………… dahil, (ast) #.

#:. lim_ (h hanggang 0) (sqrt (4 + h) -sqrt4) / h = 1/4 #.

#: "The Reqd Lim." = 1 / (1/4) = 4 #.

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