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Let $f(x)=\sqrt{x}.$ Which of the following values of $\delta$ guarantee that if $|x-4|<\delta$ then:

$$|f(x)-2|<\frac{1}{8}?$$

A

$\cfrac{1}{1000}$

B

$\cfrac{1}{100}$

C

$\cfrac{1}{10}$

D

$1$

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