or a unit step input, the response of the system from an initial steady state condition at $2=0$ is shown the system $($find $K_p,,$ and E$)?$

$(3$ marks$)$

Overshoot $(OS)=$exp$(-\frac{}{\sqrt[\phantom{2}]{1-{}^2}})$; Ferrod or onvitivion $=\frac{2s}{\sqrt[\phantom{2}]{3-c}}$Solve

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$3$ of $6$

$1$

$3.(16$pts$)$ Compute the following limits$,$ if they exist. If they do not exist, prove your answer.

$($a$)\underset{(x,y)(-1,2)}{lim}\sqrt[\phantom{2}]{\frac{x^2{y}^2}{y-x}}$

$($b$)\underset{(x,y)(1,1)}{lim}\frac{2x^2-2y^2}{x-y}$

$($c$)\underset{(x,y)(0,0)}{lim}\frac{x^{2}y2x{y}^2}{x^3{y}^3}$

$($d$)\underset{(x,y)(0,0)}{lim}\frac{cos(2x^{2}2y^2)-1}{x^2{y}^2}$

$2$

$4.(8$pts$)$ A particle's acceleration in space at time $t$ is given by $a(t)=.$ The initial

velocity and position at time $t=0$ is given respectively by $v(0)=($:$1,0,0$:$)$ and $r(0)=($:$0,1,0$:$).$

Find the position function vector $r$