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

Answer 1

Paisley Johnson

#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#

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Answer 2

Ezra Adams

If the limit of f(x) is 27 as x approaches c, then the limit of (f(x))^(3/2) as x approaches c is (27)^(3/2), which simplifies to 729.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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

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