32. \( y=\operatorname{sen} x-x \cos x+x^{2}+4 x+3 \) Solucion: \( x \operatorname{sen} x+2 x+4 \)

Mostrar que toda función definida en el intervalo \( f:[0,1] \rightarrow[0,1] \) tiene un punto fijo

\( \lim _ { x \rightarrow \infty } \frac { \sqrt { x ^ { 6 } - 3 x + 1 } } { 2 x ^ { 2 } + 3 x + 1 } \)

\( f(x)=1-x^{2 / 3} \) \( f(-1)=0 \) \( f(1)=0 \) Find \( f(-1) \) and \( f(1) \). \( c=\square \) values \( c \) in \( (-1,1) \) such that \( f^{\prime}(c)=0 \). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.

IV. Lia droite \( y-x-1-0 \) est une asymptote de la courbe representative \( \mathrm{f}(\mathrm{x})=\frac{\mathrm{x}^{2}+6 \mathrm{x}+2}{\mathrm{x}+1} \) si \( \mathrm{b}= \) \( \begin{array}{lllll}\text { 1. }-1 & 2.3 & 3.2 & 4 .-3 & 5 . \frac{2}{3}\end{array} \)

\( \frac{d}{dx}|x^{3}-\cos (x)| \)