How do you evaluate the limit #root6(2x-14)# as x approaches #7#?

1 Answer
Jim H
Oct 28, 2016

We can reason as follows:

As #x# gets closer and closer to #color(red)7#,

#2x# gets closer and closer to #2xxcolor(red)(7)# which is #color(orange)14#, so

#2x-14# gets closer and closer to #color(orange)(14)-14# which is #color(green)0#, and

#root(6)(2x-14)# gets closer and closer to #root(6)color(green)0# which is #0#,

In the end we got the same thing as we would get by substituting #7# for #x#.

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