Tuesday

September 23, 2014

September 23, 2014

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

use local linearization to estimate g(2.05)

is your estimate too high or too low?

- Calculus -
**drwls**, Friday, December 21, 2012 at 6:59pmg(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

**Answer this Question**

**Related Questions**

Calculus - Find the local linearization of f(x) near x=0 and use it to ...

Calculus - What is the local linearization of e^x^2 near x=1? Is the answer 1+2x

math - 1-show that 1-x/2 is the tangent line approximation to 1/ sqrt of 1+x ...

Calculus - Find the linearization of f(x)= sqrtx at x=25 and use the ...

CALC (TANGENT LINE) - 1-show that 1-x/2 is the tangent line approximation to 1/ ...

Calculus - 1) Find the linearization of f(x) = sin(x) at x = 0 AND use it to ...

calculus - Use the linearization approximation (1+x)^k=1+kx to find an ...

calculus - Use the linearization approximation (1+x)^k=1+kx to find an ...

Calculus - The linearization at a=0 to sqrt(1+6x) is A+Bx where A is: ____ and ...

Calculus - Suppose f(x) is differentiable at x=a. What does tangent line ...