G 7.In class we derived the equations for a projectile under the force of gravity and linear drag~x(t) =u0τ[1−e(−tτ)]ˆi+{(gτ2+w0τ)[1−e(−tτ )]−gτt}ˆkwhereτ=mCD, the drag time, gis the acceleration of gravity and (u0,w0) are the components of the initialvelocity(a)Findz(x).(b)Compu te the Maclaurin series ofz(x). LetzM(x) be the Maclaurin series up to cubic terms inx.(c)What is the radius of convergence of the Maclaurin series?(d)Notice that as the drag cofficient goes to zero,τ→[infinity]. It’s really not obvious from the parameterization thatz(x) has a limit asτ→ [infinity]. Find the limit and call the functionz∗(x). You can use the Maclaurin series tohelp you.(e)Plotz(x),zM(x),z∗(x) labeling the maxima of each curve. Describe the differences.(f)The "range of the projectile" is the horizontal distance it travels before it hits the ground again. Find therange of the approximate trajectoryzM(x), the range of the drag-free trajectory, z∗(x). ( I think the rangeof the actual trajectory is too complicated.