Linear Approximation help please?

Question

The numbers Rsub1, Rsub2, and Rsub3 and R satisfy the following equation: (1/Rsub1)+(1/Rsub2)+(1/Rsub3)=(1/R).

A. If Rsub1=1 and Rsub2=2 and Rsub3=3, compute R exactly.
B. If both Rsub1 and Rsub2 are held constant, and Rsub3 is increased by .05, what is the approximate change in R?

Ok, I got part a, that's simple enough. I realize you can solve this easily using a calculator, But how do you do B by using linear approximation?

Answer 1

In essence, you're being asked for a linear approximation of
f(x) = 1/1 + 1/2 + 1/x near x=3. Use differentials:

Δf ≈ df = f'(x)dx

f'(x) = -x^(-2); f'(3) = -1/9

dx = Δx = 0.05

So df = (-1/9)*0.05 ≈ -0.00556