Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

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We will use the following limit rules for this problem: $\ Rule -\ 1 \ : \lim\limits_{x \to a} [A(x)]^n =[\lim\limits_{x \to a} A(x)]^n$ $\ Rule \ - \ 2 : \lim\limits_{x \to a} A(x)=A(a)$ Apply the given rules: $\lim\limits_{x\to 1}(\sqrt {1-x^2})=[\lim\limits_{x\to 1}\sqrt {1-x^2}]\\=\sqrt {1-1^2} \\=\sqrt {0}\\=0$