How do I evaluate this limit using Limit Laws?

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

1 Answer
Jim H
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#

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