(b) Determine the modulus and argument of \( c^{5} \), where \( c=1+i \sqrt{3} \). \( \quad \begin{array}{c}c^{2}=1+i \sqrt{3} \\ c^{5}=1+\end{array} \) (c) Show that \( \int_{C} \exp \left(\frac{1}{z^{2}}\right)=0 \) where \( C \) is the unit circle \( |z|=1 \)

8. \( \int \frac{8 x^{2} d x}{\left(x^{3}+2\right)^{3}} \)

Round your answers to the nearest thousandth. Do not round any intermediate computations. \[ \ln \frac{3}{4}=\square \] \( \ln 20.6=\square \)

Consider the following. \[ \begin{array}{l}y=x^{2} \\ y \\ y \\ y\end{array} \] (b) Use the integration capabilities of the graphing utility to approximate the area to four de

Soit \( f \) la fonction définle sur un domaine de dȩ̀inition par \( f(x)=\frac{1}{5}\left(-\sqrt{x} e^{-4 x}\right) \). On admettra que \( f \) est dérivable deux fois sur chaque intervalle contenu dans son domaine de définition. Donner la dérivée de \( f \).

Find the Maclaurin series for the following function and determine its radius of convergence \( R \). \( f(x)=\ln \left(\frac{1+x}{1-x}\right) \). \( R=\square \) Use the first four terms of the series to approximate \( \ln (3) \). (Round your answer to six decimal places.) \( \ln (3) \approx \square \)