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Examine the continuity of the following ...

Examine the continuity of the following functions at indicated points.
`f(x)={((x^2-a^2)/(x-a),if xnea` `atx=a),(a, ifx=a):}`

Text Solution

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`lim_(xtoa)f(x)=lim_(xtoa)(x^2-a^2)/(x-a)`
`lim_(xtoa)((x-a)(x+a))/(x-a)`
`lim_(xtoa)(x+a)=2a`
Now f(a)=a
Hence `lim_(xtoa)f(x)nef(a)`
So f(x)is not continuous at x=a
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