Question

Найдите f'(пи)+f(пи)+2, если f(x)=x*sin2x

Answer 1

$f(x)=x\cdot sin2x\\\\f(\pi )=\pi \cdot sin2\pi =0\\\\f'(x)=sin2x+2x\cdot cos2x\\\\f'(\pi )=sin2\pi +2\pi \cdot cos2\pi =0+2\pi \cdot 1=2\pi \\\\f'(\pi )+f(\pi )+2=2\pi +0+2=2\pi +2=2(\pi +1)$

Answer 2

Ответ:2+2π

Объяснение:

f'(x)=sin2x+2x*cos2x

f'(π)+f(π)+2=sin2π+2π*cos2π+π*sin2π=2π+2