27.   Find \lim_{x \rightarrow 5 } f (x) , where f( x) = |x| -5

Answers (1)

\lim_{x \rightarrow 5 } f (x) , where f( x) = |x| -5

The right-hand Limit or  Limit at x=5^+

\lim_{x \rightarrow 5^+} f (x) = \lim_{x \rightarrow 5^+} |x|-5=5-5=0

The left-hand limit or Limit at x=5^-

\lim_{x \rightarrow 5^-} f (x) = \lim_{x \rightarrow 5^-}|x|-5=5-5=0

Since Left-hand limit and right-hand limit are equal, The limit of this function at x = 5 is 0.

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