If limit of #f(x)=4# as #x->c#, what the limit of #f(x)^(3/2)# as #x->c#?

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Answer 1 · 2018-04-03T19:57:35

# 8#.

Prerequisite : Suppose that, #lim_(x to a)F(x)=l#. If #G# is

continuous at #l#, then,

#lim_(x to a)(G@F)(x)=lim_(x to a)G(F(x))=G(lim_(x to a)F(x))=G(l)#.

Given that, #lim_(x to c)f(x)=4#.

Now, #G(x)=x^(3/2)# is continuous on #RR, &,#

#(G@f)(x)=G(f(x))=(f(x))^(3/2)#.

#:. lim_(x to c){f(x)}^(3/2)#,

#=lim_(x to c)(G@f)(x)#,

#=G(lim_(x to c)f(x))#,

#=G(4)#.

# rArr lim_(x to c)(f(x))^(3/2)=4^(3/2)=(2^2)^(3/2)=2^3=8#.