The right hand limit of the function $f(x) = \left\{ {\begin{array}{*{20}{l}} {\frac{{|x - 4|}}{{x - 4}},}&{x \ne 4}\\ {0,}&{x = 4} \end{array}} \right.$ at $x=4$, is

JEE MATHEMATICS MCQ: LIMITS

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The right hand limit of the function

f(x) = \left\{ {\begin{array}{llllllllllllllllllll} {\frac{{|x - 4|}}{{x - 4}},}&{x \ne 4}\\ {0,}&{x = 4} \end{array}} \right.

x=4

, is

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Correct option: A

Option A (1) is correct because the right-hand limit is calculated by considering values of x approaching 4 from the right, where the absolute value simplifies to the expression itself.

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