Spørsmål # 15ada

Spørsmål # 15ada
Anonim

Svar:

#lim_ (x-> 0) x / sqrt (1-cos (x)) = sqrt (2) #

Forklaring:

# lim_ (x-> 0) x / sqrt (1-cos (x)) #

# = Lim_ (x-> 0) x / sqrt (1-cos (x)) * sqrt (1 + cos (x)) / sqrt (1 + cos (x)) #

# = Lim_ (x-> 0) (xsqrt (1 + cos (x))) / sqrt (1-cos ^ 2 (x)) #

# = Lim_ (x-> 0) (xsqrt (1 + cos (x))) / sin (x) #

# = Lim_ (x-> 0) x / sin (x) sqrt (1 + cos (x)) #

# = Lim_ (x-> 0) x / sin (x) * lim_ (x-> 0) sqrt (1 + cos (x)) #

# = 1 * sqrt (2) #

# = Sqrt (2) #