\( \frac{d^{5} u}{d r^{5}}+5 \frac{d^{4} u}{d r^{3}}-10 \frac{d^{2} u}{d r^{2}}+\frac{d u}{d r}+5 u=0=Y h=C l e^{0 x}+C 2 x e^{0 x}+C 3 e^{-0.5 x}+ \) \( e^{2 x}(c 4 \cos 2 x+C 5 \operatorname{sen} 2 x) \) Verdadero Falso

\( \lim _ { ( x , y ) \rightarrow ( y , 3 ) } \frac { \sqrt { x } - \sqrt { y + 1 } } { x - y - 1 } \)

If \( y=\sqrt{x}-\frac{1}{\sqrt{x}} \quad \) prove that \( 2 x \frac{d y}{d x}+y=2 \sqrt{x} \)

\( y _ { 2 } ( x ) = c x ^ { 4 } \sum _ { n > 1 } ^ { \infty } c _ { n } x ^ { n } \ln x + x \sum _ { n = 0 } ^ { \infty } b _ { n } x ^ { n } \)

Cos \( \mathrm{x}=1-\frac{x^{2}}{2!}+\frac{x^{4}}{4!}-\frac{x^{6}}{6!}+\ldots \ldots \) Show that \( \mathrm{y}=\frac{\ln x}{x} \) has maximum value at \( \mathrm{x}=\mathrm{e} \)

The final result of \( \lim _{x \rightarrow 16}\left(\frac{\sqrt{x}-4}{x-16}\right)=1 / d \)