1. ## Linearization Help Please

know the linearization L(x)=f(a)+deriv (a)(x-a) is originally the tangential line to f at x=a. So, we think that for x near a, L(x)=f(x). While the change in y=f(x)-f(a)=deriv f(a).

Change in x=deriv f(a)(x-a)
Change in y=d=L(x)=f(x)=deriv f(a)dx
dx=change x=(x-a)

Even with all this i still can't get these problems..

a.)Find the linearization of y=f(x)=sqr(1+x) at x=0

b.) Find dy

c.) Find dy when x=0 and dx=.2

d.) Estimate f(.2) by the linearization

thanks for your help!

2. Originally Posted by mcdaking84
know the linearization L(x)=f(a)+deriv (a)(x-a) is originally the tangential line to f at x=a. So, we think that for x near a, L(x)=f(x). While the change in y=f(x)-f(a)=deriv f(a).

Change in x=deriv f(a)(x-a)
Change in y=d=L(x)=f(x)=deriv f(a)dx
dx=change x=(x-a)

Even with all this i still can't get these problems..

a.)Find the linearization of y=f(x)=sqr(1+x) at x=0

The linearisation is:

$f(x)=f(0)+f'(0)x$

where:

$f(0)=\sqrt{1}=1$

also:

$f'(x)=(1/2) (1+x)^{-1/2}$

so:

$f'(0)=1/2$

CB