1.

Examine the continuity of the following functions at indicated points. f(x)={((x^2-1)/(x-1)ifxne1 at x=1),(2if x=1):}

Answer»

Solution :`F(x)=(x^2-1)/(x-1)`
`lim_(xto1)f(x)=lim_(xto1)(x^2-1)/(x-1)=lim_(xto1)(x+1)=2`
`f(1)=2`
Hence `lim_(xto1)f(x)=f(1)` and
so f(x) is CONTINUOUS at x=1


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