How do you evaluate the limit $\sqrt[6]{2 x - 14}$ $root6(2x-14)$ as x approaches $7$ $7$ ?

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How do you evaluate the limit $\sqrt[6]{2 x - 14}$ $root6(2x-14)$ as x approaches $7$ $7$ ?

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Answer 1 · 2016-10-28T17:31:14

We can reason as follows:

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

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

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

$\sqrt[6]{2 x - 14}$ $root(6)(2x-14)$ gets closer and closer to $\sqrt[6]{0}$ $root(6)color(green)0$ which is $0$ $0$ ,

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

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How do you evaluate the limit $\sqrt[6]{2 x - 14}$ $root6(2x-14)$ as x approaches $7$ $7$ ?

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