If limit of f(x)=27f(x)=27 as x->cxc, what the limit of (f(x))^(3/2)(f(x))32 as x->cxc?

1 Answer
Jul 17, 2017

81sqrt3813 (assuming you really want (f(x))^(3/2)(f(x))32

Explanation:

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