gnatopoditw

2022-06-24

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

Schetterai

Beginner2022-06-25Added 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

Beginner2022-06-26Added 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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My steps:

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