For what value of a is this function `f(x){:{((x^4-1)/(x-1)if,x ne 1),(aif,x=1):}`continuous at x=1?

Explanation

LHL of f(x) at x=4 is
`underset(xto4^(+))limf(x)=underset(hto0)limf(4-h)`
`=underset(hto0)lim(|4-h-4|)/(4-h-4)=underset(hto0)lim(|-h|)/(-h)`
`=underset(hto0)limh/-h=underset(hto0)lim-1`
`=-1`
`RHL " of " f(x) " at "x=4" is"`
`underset(xto4^(+))limf(x)=underset(hto0)limf(4+h)`
`=underset(hto0)lim(|4+h-4|)/(4+h-4)`
`=underset(hto0)lim(|h|)/(h)=underset(hto0)limh/h=underset(hto0)lim1`
`=1`