If `(x^2+x-2)/(x+3)lt=(f(x))/(x^2)lt=(x^2+2x-1)/(x+3)` hold for a certain interval containing the point `x=-1a n d("lim")_(xvec1)f(x)e xi s t s` then find the value of `("lim")_(xvec-1)f(x)`

Answer

-1

Explanation

`(x^(2)+x-2)/(x+3)le(f(x))/(x^(2))le(x^(2)+2x-1)/(x+3)`
or `underset(xto-1)lim(x^(2)+x-2)/(x+3)leunderset(xto-1)lim(f(x))/(x^(2))leunderset(xto-1)lim(x^(2)+2x-1)/(x+3)`
or` 1-leunderset(xto-1)lim(f(x))/(x^(2))le-1`
or`underset(xto-1)lim(f(x))/(x^(2))=-1" "`(Using Sandwich theorem)
or`(underset(xto-1)limf(x))/(underset(xto-1)limx^(2))=-1`
or `underset(xto-1)limf(x)=-underset(xto-1)limx^(2)=-1`