Symmetry and Asymptotes then Sketching of Curve

Show that the graph of the function $f\left(x\right)=x^5$ is symmetric with respect to the Origin

Show that the graph of the function $f\left(x\right)=x^3+x$ is symmetric with respect to the Origin

Show that the graph of the function $f\left(x\right)=2x^3-4x$ is symmetric with respect to the Origin

Show that the graph of the function $f\left(x\right)=x^3$ is symmetric with respect to the Origin

Show that the graph of the function $f\left(x\right)=x^5+x^3+x$ is symmetric with respect to the Origin

The length of the shadow of a pole inclined at $10°$ to the vertical towards the sun is $2.05$ metres, when the elevation of the sun is $38°$. The length of the pole is

Compute the area of the region bounded by the curve $y=ex{\log }_{e}x$ and $y=\frac{{\log }_{e}x}{ex}$ where $\ln e=1$