5. Find a power series for f(x)=ln x, centered at 1, and determine the interval of convergence.

3. The pressure drop, $\Delta p$, for incompressible turbulent flow in a horizontal round pipe of diameter $D$ can be written in functional form as \[ \Delta p = F(V, D, l, \epsilon, \mu, \rho) \] where $V$ is the average velocity, $l$ is the pipe length, $\epsilon$ is a measure of the roughness of the pipe wall, $\rho$ and $\mu$ are fluid density and viscosity, respectively. Find a non-dimensional relationship for $\Delta p$. (use $\rho, V, D$ as repeating variables) (20%)

5. Find a power series for f(x)=ln x, centered at 1, and determine the interval of convergence.

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