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Linearization problem

by grothem
Tags: linearization
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grothem
#1
Feb7-11, 09:50 PM
P: 23
1. The problem statement, all variables and given/known data
Linearize the equation

Vout = (10^v)*sin(x)

about x=0,0.1, and 1. Write the equation in both the original coordinates and the shifted (linearized) coordinates.


2. Relevant equations
y=f(a)+f'(a)(x-a)


3. The attempt at a solution
dVout/dx = (10^v)*cos(x)
evaluating that equation at x=0,0.1, and 1 gives me
10^v, 10^v*(.995), and 10^v*(.54) , respectively
therefore, Vout = 10^v*sin(0)+10^v*(x-0) for x=0, and similar for x=0.1, and 1. This doesn't seem right though, and I'm not sure how to write the equation in the shifted coordinates.
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