Question

what is the error in linear approximation when f(x)=sqrt(3+x) a=22 and delta x= .5

Answer 1

First of all, what's the linear approximation of your function when a=22?

Answer 2

5+1/10(x-22)??

Answer 3

The error is given by delta(x)*(dy/dx at x=a).

Answer 4

so it would be (.5)*5?

Answer 5

no thats not right how do i find derivative at x=a?

Answer 6

First, find f'(x), then substitute x=a there. :D

Answer 7

i got 1/10 for f^1 of (x)

Answer 8

Then just multiply that by 0.5 and that's the error. :D

Answer 9

f(a+.5) - the linear approx of f(a+.5)

Answer 10

f(x)=sqrt(3+x) a=22 and h = .5
f(a) = sqrt(25) = 5

f'(a) = 1/2sqrt(3+a) = 1/10

y = 1/10(22+.5-22) + 5

y = 5.05

f(25.5) - 5.05 = error