$f(x,y)=\surd (7+2xy)$Find the linear approximation at $(3,-1)$

gnatopoditw
2022-06-24
Answered

$f(x,y)=\surd (7+2xy)$Find the linear approximation at $(3,-1)$

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Schetterai

Answered 2022-06-25
Author has **25** answers

make a change of variable $x=3+h,y=-1+k.$. then

$z={(7+2(3+h)(-1+k))}^{1/2}={(1-2h+6k+\cdots )}^{1/2}=1+\frac{1}{2}(-2h+6k)+\cdots =1-h+3k+\cdots $

the planar approximation of $z$ at $(3,-1)$ is $z=1-(x-3)+3(y+1).$

$z={(7+2(3+h)(-1+k))}^{1/2}={(1-2h+6k+\cdots )}^{1/2}=1+\frac{1}{2}(-2h+6k)+\cdots =1-h+3k+\cdots $

the planar approximation of $z$ at $(3,-1)$ is $z=1-(x-3)+3(y+1).$

Devin Anderson

Answered 2022-06-26
Author has **6** answers

Use

$L(x)-f(3,-1)=-(x-3)+3(y-(-1))=3-x+3y+3.$

$L(x)-f(3,-1)=-(x-3)+3(y-(-1))=3-x+3y+3.$

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$1/(1+2x{)}^{4}\approx 1\u20138x$

how do I determine its accuracy?

$1/(1+2x{)}^{4}\approx 1\u20138x$

how do I determine its accuracy?

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