How do I evaluate this limit using Limit Laws?

lim_(x->8)(x+28)^(1/2)/(x+19)^(2/3)

1 Answer
Jan 18, 2018

Please see below.

Explanation:

Ultimately, the limit laws tell us that we can find this limit by substituting 8 for x. But, probably the real question is how do they do that?

lim_(x->8)(x+28)^(1/2)/(x+19)^(2/3) = (lim_(xrarr8)(x+28)^(1/2))/(lim_(xrarr8)(x+19)^(2/3)) if the bottom is not 0.

= ((lim_(xrarr8)(x+28))^(1/2))/(lim_(xrarr8)(x+19))^(2/3) if the bottom is not 0.

= (lim_(xrarr8)(x)+lim_(xrarr8)(28))^(1/2)/(lim_(xrarr8)(x)+lim_(xrarr8)(19))^(2/3) if the bottom is not 0.

= ((8)+28)^(1/2)/((8)+19)^(2/3) if/because the bottom is not 0

= 36^(1/2)/27^(2/3)

= 6/9 = 2/3