1 to 21. Use the Cauchy-Riemann conditions to find out whether the functions in Problems 1.1 to 1.21 are analytic. Similarly, find out whether the following functions are analytic. 24. yix x² + y²

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Consider the following hypothetical results for an experiment similar to the one you designed and conducted this past week. Refer to Part 2 of the Student Lab Guide, (page 34 on propagation of uncertainty, and pages 53-56 on statistical significance of your results) for assistance. Ben and Jerry tested the dependence of the acceleration of a cart on the net force applied to that cart (a=F/m). The cart mass was known to be 0.600 kg with negligible uncertainty. They plotted acceleration versus force and found the slope of their graph to be 1.70 +/- 0.02. Answer the following questions: (a) What are the units of their slope? Why? (b) What is the expected value of their slope? Why? (c) Is their experimental result consistent with this expected value? Why or why not?

Consider a thin hoop of mass (1.420 ± 0.001) kg and radius  (0.250 ± 0.002) m. The moment of inertia for a thin hoop rotating about an axis going through its center is MR2 . Calculate the moment of inertia of this hoop and its uncertainty using error propagation rules (see Appendix). Clearly show work.  Please solve the uncertainty using the appendix I attached