Given the differential equation \( \frac{dy}{dx} = 3y \) and the initial condition \( y(0) = 2 \), find the particular solution.

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.) \( \ln (3) \approx \square \)

\( \frac{d^{4} y}{d x^{4}} \mathrm{y}=\cos 2 x \) إذا كانت

\( \lim _ { m \rightarrow + \infty } m [ 2 - \sin ( n ^ { 2 } + 1 ) ] \)

\( y = ( \tan 3 x ^ { 4 } ) ^ { \sqrt { x + 3 } } \)

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