\[\begin{array}{l} \mathop {\lim }\limits_{x \to a} f\left( x \right) = C\\ \mathop {\lim }\limits_{x \to a} g\left( x \right) = D\\ 1)\mathop {\lim }\limits_{x \to a} x = a\\ 2)\mathop {\lim }\limits_{x \to a} k = k\\ 3)\mathop {\lim }\limits_{x \to a} [f(x) \pm g(x)] = \mathop {\lim }\limits_{x \to a} f\left( x \right) \pm \mathop {\lim }\limits_{x \to a} g\left( x \right) = C \pm D\\ 4)\mathop {\lim }\limits_{x \to a} f(x).g(x) = \mathop {\lim }\limits_{x \to a} f\left( x \right).\mathop {\lim }\limits_{x \to a} g\left( x \right) = C.D\\ 5)\mathop {\lim }\limits_{x \to a} k.f(x) = k.\mathop {\lim }\limits_{x \to a} f(x)\\ 6)\mathop {\lim }\limits_{x \to a} \frac{{f\left( x \right)}}{{g\left( x \right)}} = \frac{{\mathop {\lim }\limits_{x \to a} f\left( x \right)}}{{\mathop {\lim }\limits_{x \to a} g\left( x \right)}} = \frac{C}{D}\left( {\mathop {\lim }\limits_{x \to a} g\left( x \right) \ne 0} \right)\\ 7)\mathop {\lim }\limits_{x \to a} {[f\left( x \right)]^n} = {\left[ {\mathop {\lim }\limits_{x \to a} f\left( x \right)} \right]^n} = {C^n}\\ 8)\mathop {\lim }\limits_{x \to a} \sqrt[n]{{f\left( x \right)}} = \sqrt[n]{{\mathop {\lim }\limits_{x \to a} f\left( x \right)}} = \sqrt[n]{C}\\ 9)\mathop {\lim }\limits_{x \to a} {\left( {f\left( x \right)} \right)^{g(x)}} = {\left( {\mathop {\lim }\limits_{x \to a} f\left( x \right)} \right)^{\mathop {\lim }\limits_{x \to a} g\left( x \right)}} = {C^D} \end{array}\]
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