using matlab

We consider a column which is fixed at one end and pinned at the other end. The load under which this column buckles $("$Euler$\text{'}$s

critical load"$)$ is $F=z^2\frac{EI}{L^2}$ where $E,$I,$L$ are given $($they describe the material, cross section and length of the column$)$ and $z$

satisfies

$tanz=z$

This equation has a root $z_0=0$ and positive roots $z_1{z}_1,$dots,$z_{m}m=20(f,[a,b])a,bxtanxtogether{z}_{0}0.$ The critical buckling load $is$ obtained using $z_1.$

$(a)$ Write a program which prints out $z_1,$dots,$z_m$ with $15$ significant digits and run $it$ for $m=20.$ Use fzero $(f,[a,b])$ and

choose $a,b$ appropriately for each root. Hint: sketch the functions $x$ and $tanxtogether.$

$(b)$ Use the Newton method $to$ approximate $z_0,$ starting with a positive initial guess. $Do$ you observe linear $or$ superlinear

convergence? Explain!