All steps please Find the Taylor series for f(x) = 1/x^2 about x = -1 and find the interval of convergence

By using hamiltonian equations. Find the solution of harmonic oscillator in : A-2 Dimensions  B-3 dimensions

For each function, use our techniques to sketch the graph. Include asymptotes, at least one intercept,and a derivative chart.

The Newton–Raphson method for finding the stationary point(s) Rsp of a potential energy surface V is based on a Taylor-series expansion around a guess, R0. Similarly, the velocity Verlet algorithm for integrating molecular dynamics trajectories [xt, vt] is based on a Taylor-series expansion around the initial conditions, [x0, v0]. Both of these methods rely strictly on local information about the system. How many derivatives do we need to compute in order to apply them?