InterviewSolution
Saved Bookmarks
| 1. |
Let f(x) be a non negative continuous and bounded function for all xge0 .If (cos x)f(x) lt (sin x- cosx)f(x) forall x ge 0, then which of the following is/are correct? |
|
Answer» `f(6)+f(5)gt0` `therefore g(x)=e^(x)cosxf(x)+e^(x)(cosx-sinx)f(x)` `=e^(x)(cosxf(x)+(cosx-sinx)f(x)` `le0` `therefore g(X)` is a NON increasing function `therefore f(6)=e^(6)cos 6 f(6)le0` `therefore f(6)le0` But given that f(x) is non negative ltbegt `therefore f(6)=0` with similar reasons f(5),f(7)=0 Thus `x^(2)-3x+2+f(7)=0` or `x^(2)-3x+2=0` l has 2 distinct solution `underset(xrarr6)lim(f(x)-sin(pix))/(x-6)` =`underset(xrarr6)limf(x)-picos(pix)/(1)` (applying L hospital rule) `=f(6)-pilt0` |
|