$\"\"$

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The function $\"\\lim_{x\\rightarrow$ .

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To show that for each $\"\\epsilon$ ,there exists a $\"\\delta$ such that $\"\\left$ , whenever $\"0<\\left$ .

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Consider $\"0<\\left$

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$\"0<\\left$ .

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Consider $\"\\left$ .

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$\"\\left$

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Apply $\"\\epsilon$ , theorem

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$\"f(x)=\\infty\"$ , for $\"M>0\"$ there exists a $\"\\delta$ such that $\"f(x)>M\"$ when ever $\"c<x<c+\\delta\"$ .

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$\"\\frac{1}{x-5}>\\epsilon\"$

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Now there exist $\"M\"$ such that $\"x-5<\\frac{1}{M}\"$ .

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Now $\"x-5<\\delta\"$ .

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Now we find relation between $\"\\epsilon\"$ and $\"\\delta\"$ such that $\"\\delta$ .

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$\"x-5<\\frac{1}{M}\"$ .

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Therefore, $\"\\lim_{x\\rightarrow$ .

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$\"\"$

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$\"\\lim_{x\\rightarrow$ .