Let `f:(1,2)toR` satisfy the inequality
`(cos(2x-4)-33)/(2)ltf(x)lt(x^(2)|4x-8|)/(x-2)AAx in(1,2).`
Then find `lim_(xto2^(-)) f(x).`

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)