If limit of #f(x)=27# as #x->c#, what the limit of #(f(x))^(3/2)# as #x->c#?

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Answer 1 · 2017-07-17T17:33:55

#81sqrt3# (assuming you really want #(f(x))^(3/2)#

Roots and powers are continuous (have limits that can be found by sucstitution).

Therefore

#lim_(xrarrc)(f(x))^(3/2) = (lim_(xrarrc)f(x))^(3/2) #

# = (27)^(3/2) = (sqrt27)^3 = 27sqrt27 = 27 * 3sqrt3 = 81sqrt3#

Bonus

#lim_(xrarrc)(f(x))^(2/3) = (lim_(xrarrc)f(x))^(2/3) #

# = (27)^(2/3) = (root(3)27)^2 = 3^2 = 9#