(a) Find

(b) Use the total differential dz to approximate

Kathleen Rausch
2021-12-12
Answered

Consider the following. (Round your answers to four decimal places.)

$f(x,y)=x\mathrm{cos}\left(y\right)$

(a) Find$f(7,9)$ and $f(7.1,9.05)$ and calculate $\mathrm{\Delta}z$ .

$f(7,9)=?$

$f(7.1,9.05)=?$

$\mathrm{\Delta}z=?$

(b) Use the total differential dz to approximate$\mathrm{\Delta}z$ .

$dz=?$

(a) Find

(b) Use the total differential dz to approximate

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Foreckije

Answered 2021-12-13
Author has **32** answers

(a) Find

yotaniwc

Answered 2021-12-14
Author has **34** answers

b) ${f}_{x}=\mathrm{cos}\left(y\right)\Rightarrow {f}_{x}(7,9)=\mathrm{cos}9$

${f}_{y}=-x\mathrm{sin}\left(y\right)\Rightarrow {f}_{y}(7,9)=-7\mathrm{sin}\left(9\right)$

$dx=0.1$ , $dy=0.05$

$dz={f}_{x}dx+{f}_{y}dy=\left(0.1\right)\mathrm{cos}9+0.05(-7\mathrm{sin}\left(9\right))=-0.2354$

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