mathop {lim }limits_{x to 1} frac{1}{|1 - x|} | vedclass

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(D) To find the limit $\mathop {\lim }\limits_{x 	o 1} \frac{1}{|1 - x|}$,we examine the left-hand and right-hand limits.Left-hand limit: $\mathop {\

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$\infty$

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(D) To find the limit $\mathop {\lim }\limits_{x 	o 1} \frac{1}{|1 - x|}$,we examine the left-hand and right-hand limits.Left-hand limit: $\mathop {\lim }\limits_{x 	o 1^-} \frac{1}{|1 - x|} = \mathop {\lim }\limits_{h 	o 0^+} \frac{1}{|1 - (1 - h)|} = \mathop {\lim }\limits_{h 	o 0^+} \frac{1}{|h|} = \infty$.Right-hand limit: $\mathop {\lim }\limits_{x 	o 1^+} \frac{1}{|1 - x|} = \mathop {\lim }\limits_{h 	o 0^+} \frac{1}{|1 - (1 + h)|} = \mathop {\lim }\limits_{h 	o 0^+} \frac{1}{|-h|} = \mathop {\lim }\limits_{h 	o 0^+} \frac{1}{h} = \infty$.Since both one-sided limits approach $\infty$,the limit is $\infty$.

$\mathop {\lim }\limits_{x \to 1} \frac{1}{|1 - x|} = $

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