The function f(x), for which `f(x)={x^(2),xne1 2, x=1}`
Show that:
`lim_(x to 1) f(x)=1`

Explanation

At `x=1 `
R.H.L. `=underset(xrarr1+)"lim"f(x)=underset(hrarr0)"lim"f(1+h)`
`=underset(hrarr0)"lim"(1+h)^(2)=(1+0)^(2)=1`
L.H.L. `=underset(xrarr1-)"lim" f(x)=underset(hrarr0)"lim"f(1-h)`
`=underset(hrarr0)"lim"(1-h)^(2)=(1-0)^(2)=1`
`because R.H.L. =L.H.L.=1`
`therefore underset(xrarr1)"lim"f(x)=1`. Hence Proved.