Provide an Appropriate Response $\varepsilon > 0$ , Find an Interval $\mathrm { I } = ( 1,1 + \delta ) , \delta > 0$

Multiple Choice

Provide an appropriate response.
-Given $\varepsilon > 0$ , find an interval $\mathrm { I } = ( 1,1 + \delta ) , \delta > 0$ , such that if $x$ lies in $\mathrm { I }$ , then $\sqrt { x - 1 } < \varepsilon$ . What limit is being verified and what is its value?

A) $\lim _ { x \rightarrow 1 ^ { + } } \sqrt { x } = 1$
B) $\lim _ { x \rightarrow0 ^ { - } } \sqrt { x - 1 } = 0$
C) $\lim _ { x \rightarrow \mathbf { 1 } ^ { + } } \sqrt { x - 1 } = 0$
D) $\lim _ { x \rightarrow 1 ^ { - } } \sqrt { x - 1 } = 0$