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Question
Examine the continuity of the following function :
`{:(,f(x),=(x^2-16)/(x-4),",","for "x!=4),(,,=8,",","for "x=4):}} " at " x=4`
Solution
`f(x) = (x^2-16)/(x-4),` for x ≠ 4
= 8 for x = 4
f(4) = 8
Now `lim_(x-> 4)f(x) = lim_(x-> 4) (x^2-16)/(x-4)`
`= lim_(x-> 4)((x-4)(x+4))/(x-4)`
= 8
Thus `lim_(x-> 4)f(x) = f(4)=8`
Hence function `f` is continuous at x = 4.
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