The right hand limit of the function f(x)=|x−4|x−4, x≠40, x=4at x = 4, is

A
1
B
-1
C
0
D
non-existent

Solution:

We have,

$\begin{array}{l} (RHL of f (x) at x = 4) \\ = lim_{x \to 4^{+}} f (x) = lim_{h \to 0} f (4 + h) = lim_{h \to 0} \frac{| 4 + h - 4 |}{4 + h - 4} \\ = lim_{h \to 0} \frac{| h |}{h} = lim_{h \to 0} \frac{h}{h} = lim_{h \to 0} 1 = 1 . \end{array}$

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