Question

Let `a_(1),a_(2),.......,a_(n)` be fixed real numbers and define a function `f(x)=(x-a_(1))(x-a_(2)) ......(x-a_(n))`, what is lim `f(x)`? For some `anea_(1),a_(2),.........a_(n)`, compute `lim_(Xrarr1) ` f(x)

Answer 1

`underset(xrarra_(1))"lim"f(x)= underset(xrarra_(1))"lim"[(x-a_(1)]`
`(X-a_(2))........(x-a_(n))`
`=(a_(1)-a_(1))(a_(1)-a_(2))......(a_(1)-a_(n ))=0`
If `anea_(1),a_(2),a_(3).........a_(n)` then
`underset(Xrarra)"lim"f(x)=underset(Xrarra)"lim"[x-a_(1)(x-a_(2))........(x-a_(n))]`
`=(a-a_(1))(a-a_(2))......(a-a_(n))`