Question

1.) ( lim _{x rightarrow pi / 4} frac{2 sqrt{2}-(cos x+sin x)^{3}}{1-sin 2 x} )
( frac{0}{0} ) form a plely l'Hopital's rule
( =lim _{x rightarrow pi / 4} frac{left.|ln x| 2 sqrt{2}-(cos x+sin x)^{3}right]}{d x cdot[1-sin 2 x]} )
( =lim _{x rightarrow pi / 4} frac{-3(cos x+sin x)^{2} cdot(-sin x+cos x)}{operatorname{tg} cos 2 x} )
Again ( frac{0}{0} ) form is Apply L'H sule:
( =lim _{x rightarrow pi / 4}left[frac{6(cos x+sin x)(cos x-sin x)^{2}+3(cos x+sin x)^{2}left(-cos x-sin ^{2} xright)}{-4 sin 2 x}right. )
( frac{left(Y_{J 2}+Y_{sqrt{2}}right)left(Y_{Gamma_{2}}-Y_{Gamma 2}right)^{2}+3left(1 / sqrt{2}+Y_{Omega}right)^{2}left(-1 / 8_{2}-Psi_{Gamma_{2}}right)}{-4 sin pi_{2}} )
( 0+3(2 / sqrt{2})^{2}(-2 sqrt{3}) )
-4
( =3 times 2 times-7 / sqrt{2} )
( -x )
( =-frac{3}{sqrt{2}} )

# . lim 22 -(cosx + sin x 1-sin 2x 12 sina

Solution