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Following are some important properties that help to calculate limits:

  • $ \lim_{x\to a}\Big[f(x)\pm g(x)\Big]=\lim_{x\to a}f(x)\pm\lim_{x\to a}g(x) $
  • $ \lim_{x\to a}\Big[c\cdot f(x)\Big]=c\cdot\lim_{x\to a}f(x) $
  • $ \lim_{x\to a}\Big[f(x)\cdot g(x)\Big]=\lim_{x\to a}f(x)\cdot\lim_{x\to a}g(x) $
  • $ \lim_{x\to a}\frac{f(x)}{g(x)}=\frac{\lim\limits_{x\to a}f(x)}{\lim\limits_{x\to a}g(x)}:\quad\text{ if }\lim_{x\to a}g(x)\ne0 $
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