Question

Me ajudem por favor, obrigada kkk

Answer 1

$\underset{x\to\frac{\pi}{2}}{lim}~[2sen(x)-cos(x)+cotg(x)]~=~\underset{x\to\frac{\pi}{2}}{lim}~[2sen(x)-cos(x)+\frac{cos(x)}{sen(x)}]\\\\\\\underset{x\to\frac{\pi}{2}}{lim}~[2sen(x)-cos(x)+\frac{cos(x)}{sen(x)}]~=~[2~.~sen(\frac{\pi}{2})-cos(\frac{\pi}{2})+\frac{cos(\frac{\pi}{2})}{sen(\frac{\pi}{2})}]$

$[2~.~sen(\frac{\pi}{2})-cos(\frac{\pi}{2})+\frac{cos(\frac{\pi}{2})}{sen(\frac{\pi}{2})}]~=~[2~.~1~-~0~+~\frac{0}{1}]$

$[2~.~1~-~0~+~\frac{0}{1}]~=~\boxed{2}$