Question

Questão de limite com a resposta mais detalhada possível por favor.

Answer 1

Olá!

Note que

$\cos\left(\dfrac{\pi}{4}\right)=\dfrac{\sqrt{2}}{2}=\sin\left(\dfrac{\pi}{4}\right)\Rightarrow \tan\left(\dfrac{\pi}{4}\right)=\dfrac{\sin\left(\frac{\pi}{4}\right)}{\cos\left(\frac{\pi}{4}\right)}=\dfrac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}}=1.$

Logo,

$\displaystyle \lim_{x\to\frac{\pi}{4}}\dfrac{\cos(x)-\sin(x)}{\tan(x)}=\dfrac{\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}}{1}=\dfrac{0}{1}=0.$

Bons estudos!