Pitanje # 15ada

Pitanje # 15ada
Anonim

Odgovor:

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

Obrazloženje:

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

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