Question

Calc 2 question involving total differential

Answer 1

ok so basically the total resistance R of two resistors connected in parallel circuit is given by 1/R = 1/R1 + 1/R2 and i have to approximate the change in R as R1 decreases from 12 ohms to 11 ohms and R2 increases from 10 ohms to 11 ohms

Answer 2

\[\frac{ 1 }{ R } = \frac{ 1 }{ R1 } + \frac{ 1 }{ R2 }\]

Answer 3

so i let R be denoted by z, R1 be denoted by x, and R2 denoted by y

Answer 4

\[\frac{ 1 }{ z } = \frac{ 1 }{ x } + \frac{ 1 }{ y }\]

Answer 5

solving for just z gives me

Answer 6

\[z=\frac{ 1 }{ \frac{ 1 }{ x } + \frac{ 1 }{ y }}\]

Answer 7

ok so i would just differentiate with respect to x and then with respect to y

Answer 8

\[fx(x,y) = \frac{ 1 }{ x^2(\frac{ 1 }{ x } +\frac{ 1 }{ y })^2}\]

Answer 9

\[fy(x,y) = \frac{ 1 }{ y^2(\frac{ 1 }{ x } + \frac{ 1 }{ y })^2 }\]

Answer 10

the problem is im getting really off number from the actual answer when i approximate