Let `f:(1,2)vecR` satisfies the inequality `(cos(2x-4)-33)/2ltf(x)lt(x^2|4x-8|)/(x-2)AAx in (1,2)dot` Then find `lim_(x->2^-)f(x)dot`

Answer

-16

Explanation

`(cos(2x-4)-33)/(2)ltf(x)lt(x^(2)|4x-8|)/(x-2)`
or `underset(xto2^(-))lim(cos(2x-4)-33)/(2)ltunderset(xto2^(-))limf(x)ltunderset(xto2^(-))lim(x^(2)|4x-8|)/(x-2)`
or `-16ltunderset(xto2^(-))limf(x)ltunderset(xto2^(-))lim(x^(2)(8-4x))/(x-2)`
or `-16ltunderset(xto2^(-))limf(x)lt-16`
or `underset(xto2^(-))limf(x)=-16` (by sandwich theorem)