If $\frac{d}{d x}\left\{\left(\frac{x-1}{x-\sqrt{x}}\right) e^{2 x+1}\right\}=\frac{x-1}{x-\sqrt{x}} e^{2 x+1} f(x)$, then $f(4)=$

If $y=\left(\sin ^{-1} x\right)^2$, then $\left(1-x^2\right) \frac{d^2 y}{d x^2}-x \frac{d y}{d x}=$

The radius of a cone of height 9 units is changed from 2 units to 2.12 units. The exact change and approximate change in the volume of the cone are respectively

The local maximum value $l$ and local minimum value $m$ of $f(x)=\frac{x^2+2 x+2}{x+1}$ in $R-\{-1\}$ exist at $\alpha, \beta$ respectively, then $\frac{l+m}{\alpha+\beta}=$