Let $f(x,y,z)=x+yz$ and let $Cbe$ the line segment from $P=(0,0,0)to(9,2,4).$

$(a)$ Calculate $f(r(t))$ and $ds=||r^{\text{'}}(t)||dt$ for the parameterization $r(t)=($:$9t,2t,4t$:$)$ for $0t1.$

$(Use$ symbolic notation and fractions where needed.$)$

$f(r(t))=9t+8t^2$

Correct Ans

$ds=\sqrt[\phantom{2}]{101}$

Correct Answer

$(b)$ Evaluate ${\displaystyle \underset{c}{\overset{\phantom{}}{}}}f(x,y,z)ds.$

$(Use$ decimal notation. Give your answer $to$ three decimal places.$)$