The function $u(x,t)=\frac{1}{\sqrt[\phantom{2}]{4t}}$exp$(-\frac{x^2}{4t})is$ a solution $of$ the heat equation

$\frac{\text{d}\text{e}\text{l}\text{u}}{\text{d}\text{e}\text{l}\text{t}}=\frac{de{l}^{2}u}{del{x}^2}$

Use linearization $to$ approximate the change $inu(x,t)$ when $x$ changes from $x=1to$

$x=1\mathrm{.}4$ and $t$ changes from $t=1tot=1\mathrm{.}05.$ Give your answer $to$ three decimal places.