Question

The function f(x) = 1 + x (sin x ) [cos x], 0 < x ,where [.] represents greatest integer function

• A. is continuous on $(0,\frac{\pi }{2})$
• B. is strictly decreasing in $(0,\frac{\pi }{2})$
• C. is strictly increasing in $(0,\frac{\pi }{2})$
• D. has global maximum value 2

Answer 1

The correct option is A is continuous on $(0,\frac{\pi }{2})$

In the given interval $(0,\frac{\pi }{2})$
[cos x] = 0
$\therefore$ f(x) = 1