Linearization = Example: y = 5x3 2x Taylor series expansion about Xo: $(z) = f(ro) + f'(ro)(x 1.) + } }"(7)(x = r.) + ... f(n)(xro)(x r.)n+1 5x2 2x, + (1522 - 2) (r x.) Now y is linear with respect to x -1023+ (1522 2)x (nonlinear with respect to xo). 1 n! y y + 10x = 15x2 - 2 Example: Solve for x such that y=2. 1. Guess Xo 2. Calculate new value for x. 3. if |x-xol > & then Xo=x, return to step 2. Otherwise, done! k x 1 1 0.9231 2 0.9231 0.9151 3 0.9151 0.9150 -0.5 0.5 x