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Finding a Derivative In Exercises $39-54,$ find the derivative of the function.$$g(t)=\frac{3 t^{2}+4 t-8}{3 / 2}$$
Approximate the arc length of the curve over the interval using the Trapezoidal Rule $T_{N},$ the Midpoint Rule $M_{N},$ or Simpson's Rule $S_{N}$ as indicated.\begin{equation}y=\sin x, \quad\left[0, \frac{\pi}{2}\right], \quad M_{8}\end{equation}
Approximate the arc length of the curve over the interval using the Trapezoidal Rule $T_{N},$ the Midpoint Rule $M_{N},$ or Simpson's Rule $S_{N}$ as indicated.\begin{equation}y=x^{-1}, \quad[1,2], \quad S_{8}\end{equation}
Approximate the arc length of the curve over the interval using the Trapezoidal Rule $T_{N},$ the Midpoint Rule $M_{N},$ or Simpson's Rule $S_{N}$ as indicated.\begin{equation}y=e^{-x^{2}}, \quad[0,2], \quad S_{8}\end{equation}
Find the arc length of the curve shown in Figure 12.
In Exercises $33-40,$ compute the surface area of revolution about the $x$ -axis over the interval.\begin{equation}y=x, \quad[0,4]\end{equation}
