Posted by **Clay** on Friday, December 21, 2012 at 6:41pm.

Find the local linearization of g(x)=sqrt 4x near x=2

use local linearization to estimate g(2.05)

is your estimate too high or too low?

- Calculus -
**drwls**, Friday, December 21, 2012 at 6:59pm
g(x) = sqrt 4x = 2 sqrtx

Local linearization near x = 2:

gl(x)= g(x=2) + [dg/dx@x=2])*(x-2)g

g(x=2) = 2 sqrt2

dg/dx = 2(1/2)/sqrtx = 1/sqrtx

dg/dx @ x=2 = 1/sqrt2

gl(x) = 2sqrt2 + (1/sqrt2)(x-2)

is the linearization about x = 2

For x = 2.05,

g(2.05) = 2.86356

The linearized approximation is

gl(2) + (0.05)/1.41421

= 2.8284 + 0.0353 = 2.86376

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