उत तर:
#lim_ (x-> 0) एक स / sqrt (1-cos (x)) = sqrt (2) #
स पष ट करण:
# lim_ (x-> 0) x / sqrt (1-cos (x)) #
# = Lim_ (x-> 0) एक स / sqrt (1-cos (x)) * sqrt (1 + cos (x)) / sqrt (1 + cos (x)) #
# = Lim_ (x-> 0) (xsqrt (1 + cos (x))) / sqrt (1-क य क ^ 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) #
