First slide

Introduction to limits

Question

The right hand limit of the function
$f (x) = \{\begin{cases} \frac{| x - 4 |}{x - 4}, x \neq 4 \\ 0, x = 4 \end{cases}$
at x = 4, is

Moderate

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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