Hi,

Can anybody help me out with this.........

If f(x) = x , if x is a integer

10 -x ,if x is a real number which is not an

Find whether f is continuous at x = 5.

Thanks

Arun.

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- Feb 28th 2007, 02:28 AMarunkayalContinuity
Hi,

Can anybody help me out with this.........

If f(x) = x , if x is a integer

10 -x ,*if x is a real number which is not an*

Find whether f is continuous at x = 5.

Thanks

Arun. - Feb 28th 2007, 03:10 AMticbol
Yes, f is continuos at x=5.

I don't know now, or I forgot the rules, about proving continuity. Just by reasoning/analyzing, I believe f is continuous at x = 5.

When x is not an integer, f(x) tends to be 5 coming from the left or coming from the right. At x=5, the second piece of the f is a hole because x=5 is not in the domain of that piece, for 5 is an integer.

But the first piece takes over. The hole at x=5 is filled up by the f(x) = x of the first piece. Hence x=5 is true for the piecewise f function.