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Question
Examine the following function for continuity:
f(x) = | x – 5|
Solution
Let f(x) = |x - 5|
`lim_(x->a^+) f(x) lim_(h->0) |a + h - 5| = |a - 5| = a - 5`
`lim_(x->a^-) f(x) = lim_(h->0)|a - h - 5| = |a - 5| = a - 5`
f (a) = |a - 5| = a - 5
∴ `lim_(x->a^+) f(x) = lim_(x->a^-) f(x) = f(a)`
Hence, the give function f(x) = |x - 5| is continuous.
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