# Use the linear approximation of Use the linear approximation of f(x,y)=e2x2+3y at (0,0) to estimate

Use the linear approximation of Use the linear approximation of f(x,y)=e2x2+3y at (0,0) to estimate f(0.01,−0.02). at $\left(0,0\right)$ to estimate $f\left(0.01,-0.02\right)$.
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necrologo9yh43
$\begin{array}{}\text{(This is a chain rule.)}& df=\frac{\mathrm{\partial }f}{\mathrm{\partial }x}\phantom{\rule{thinmathspace}{0ex}}dx+\frac{\mathrm{\partial }f}{\mathrm{\partial }y}\phantom{\rule{thinmathspace}{0ex}}dy.\end{array}$
$\mathrm{\Delta }f\approx \frac{\mathrm{\partial }f}{\mathrm{\partial }x}\phantom{\rule{thinmathspace}{0ex}}\mathrm{\Delta }x+\frac{\mathrm{\partial }f}{\mathrm{\partial }y}\phantom{\rule{thinmathspace}{0ex}}\mathrm{\Delta }y.$
$f\left(0+\mathrm{\Delta }x,0+\mathrm{\Delta }y\right)=f\left(0,0\right)+\mathrm{\Delta }f.$
$\begin{array}{rl}f\left(0,0\right)& =1\\ \mathrm{\Delta }x& =0.01\\ \mathrm{\Delta }y& =-0.02.\end{array}$