Find the total differential d2 for the dx = 0.01 X= 2 Y = 0 and dy = 0.01 J2 and 42 LE of function F(X₂X) = √3x + √² Compare the value,

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
Find the total differential d2 for the
dx = 0.01
X= 2, Y = 0
J2 and 12
IF
of
function F(X₂X) = √³x + √²
and dy = 0.01 compare the values
Do not
write in this
column.
Transcribed Image Text:Find the total differential d2 for the dx = 0.01 X= 2, Y = 0 J2 and 12 IF of function F(X₂X) = √³x + √² and dy = 0.01 compare the values Do not write in this column.
Expert Solution
Step 1: Given data

Given space that
the space function space is space straight f left parenthesis straight x comma space straight y right parenthesis equals square root of 3 straight x plus straight y squared end root
dx equals 0.01 comma space dy equals 0.01
formula space of space dz
dz space equals fraction numerator partial differential straight z over denominator partial differential straight x end fraction dx plus fraction numerator partial differential straight z over denominator partial differential straight y end fraction dy
fraction numerator partial differential straight z over denominator partial differential straight x end fraction equals fraction numerator partial differential square root of 3 straight x plus straight y squared end root over denominator partial differential straight x end fraction
fraction numerator partial differential straight z over denominator partial differential straight x end fraction equals fraction numerator 3 over denominator square root of 3 straight x plus straight y squared end root end fraction
fraction numerator partial differential straight z over denominator partial differential straight y end fraction equals fraction numerator 2 straight y over denominator square root of 3 straight x plus straight y squared end root end fraction
substitute space the space above space values space in space dz
dz equals fraction numerator 3 over denominator square root of 3 straight x plus straight y squared end root end fraction dx plus fraction numerator 2 straight y over denominator square root of 3 straight x plus straight y squared end root end fraction dy
dz equals fraction numerator 3 over denominator square root of 6 end fraction 0.01 plus fraction numerator 2 left parenthesis 0 right parenthesis over denominator square root of 6 end fraction 0.01
dz equals fraction numerator 0.03 over denominator square root of 6 end fraction
bold dz bold equals bold 0 bold. bold 01224744871

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