Hvordan finner du grensen lim_ (x -> - 4) (x ^ 2 + 5x + 4) / (x ^ 2 + 3x-4)?

Hvordan finner du grensen lim_ (x -> - 4) (x ^ 2 + 5x + 4) / (x ^ 2 + 3x-4)?
Anonim

#=3/5#

Forklaring, Bruke Finne Limits Algebraisk, # = Lim_ (x -> - 4) (x ^ 2 + 5x + 4) / (x ^ 2 + 3x-4) #, hvis vi plugger # x = -4 #, vi får #0/0# skjema

# = Lim_ (x -> - 4) (x ^ 2 + 4x + x + 4) / (x ^ 2 + 4x-x-4) #

# = Lim_ (x -> - 4) (x (x + 4) 1 (x + 4)) / (x (x + 4) -1 (x + 4)) #

# = Lim_ (x -> - 4) ((x '+ 4) (x' + 1)) / ((x + 4) (X-1)) #

# = Lim_ (x -> - 4) ((x + 1)) / ((x-1)) #

#=(-3)/-5#

#=3/5#