Advanced Math Archive: Questions from August 04, 2022
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Find the domain and range of the function. \[ f(x, y)=\sqrt{64-x^{2}-y^{2}} \] Domain: \[ \begin{array}{l} \left\{(x, y): x^{2}+y^{2} \leq 64\right\} \\ \left\{(x, y): x^{2}+y^{2}2 answers -
Initial-Value Problems Solve the IVPs in Problems 11-16. 12. \( y^{\prime \prime}-4 y^{\prime}+13 y=0, \quad y(0)=1, \quad y^{\prime}(0)=0 \) 14. \( y^{\prime \prime}-y^{\prime}+y=0 \), \( y(0)=0, \3 answers -
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\( \kappa^{\kappa} 14 \). Prove a. \( 1+(\cos \theta+i \sin \theta)^{6}=2 \cos 3 \theta(\cos 3 \theta+i \sin 3 \theta) \) b. \( \frac{1+(\cos \theta+i \sin \theta)^{8}}{1+(\cos \theta-i \sin \theta)^{1 answer