Question
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?
use local linearization to estimate g(2.05)
is your estimate too high or too low?
Answers
drwls
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
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