Use suitable linear approximation to find the approximate values for given functions at the points i

veleumnihryz 2022-05-03 Answered
Use suitable linear approximation to find the approximate values for given functions at the points indicated:
f ( x , y ) = x e y + x 2
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Answers (2)

bailaretzy33
Answered 2022-05-04 Author has 15 answers
Let L ( x , y )= f ( x 0 , y 0 ) + f x ( x 0 , y 0 ) ( x x 0 ) + f y ( x 0 , y 0 ) ( y y 0 ). Then L ( x , y ) f ( x , y ). Consider ( x 0 , y 0 ) = ( 2 , 4 ). Then,
L ( x , y ) = 2 + 9 ( x 2 ) + 2 ( y + 4 ) f ( 2.05 , 3.92 ) L ( 2.05 , 3.92 ) = 2.61
Notice, from a calculator, f ( 2.05 , 3.92 ) = 2.7192
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Diya Bass
Answered 2022-05-05 Author has 20 answers
Denoting the partial derivatives by f x and f y , the formula is:
f ( x 0 + h , y 0 + k ) = f ( x 0 , y 0 ) + f x ( x 0 , y 0 ) h + f y ( x 0 , y 0 ) k + o ( ( h , k ) ) .
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