Discuss the continuity of the function f, where f is defined by`f(x)={{:(3, if0lt=xlt=1),( 4, if1 < x < 3),( 5, if3lt=xlt=10):}`

Explanation

The given function is defined at all points of the interval [0,10].
Let c be a point in the interval [0,10].



Case I :



If `O<=c<1` , then `f(c)=3` and

`lim_(xrarrx)f(x)=lim_(xrarrc)(3)=3`


`:.lim_(xrarrc)f(x)=f(c)`



...