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Question
Examine the following function for continuity:
f(x) = |x – 5|
Sum
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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 given function f(x) = |x − 5| is continuous.
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