You approximate $f(t)=e^t$ by a Taylor polynomial of degree $2$ about $t=0$ on the interval $0,0\mathrm{.}5.$

$($a$)$ Is the second$-$degree Taylor approximation an overestimate or an underestimate?

overestimate

underestimate,

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$($b$)$ Use the Lagrange Error Bound for $P_n(x)$ to bound the error. Check your answer graphically on a computer or calculator.

Round your answer to three decimal places.

Error bound $=$