Question

Linear approximation - calculus help

Answer 1

Find the linear approximation of the function f(x) = sqrt(1-x) at a = 0 and use it to approximate the numbers sqrt(0.9) and sqrt(0.99).

Answer 2

Here's what I have so far:
f(0) = 1
f'(x) = 1/2(1-x)(-1)
f'(0) = -1/2
L(x) = 1/2x - 1/2
Is everything right so far?

Answer 3

This bit:

L(x) = 1/2x - 1/2

doesn't make sense

Answer 4

For that, I tried to make a tan equation...
y + 1/2 = -1/2(x - 0)
which gives y = -1/2x - 1/2
.... what should I have done?

Answer 5

@calculusxy you know calculus right? :D

Answer 6

translate as "find the equation of the line tangent to the curve

Answer 7

you got the point \((0,1)\)
you need the slope, which means first you need \(f'\)
did you get that?

Answer 8

Yeah, did you see the work I posed above?

Answer 9

L(x) = f(a) +f'(a) *(x-a)

Answer 10

Now, just replace x =0.9, you have L (0.9)
or x =0.99 to get L(0.99).
dat sit

Answer 11

at a=0, L(x) = 1-(1/2) x.

Answer 12

Shouldn't L(x) be y = -1/2x - 1/2 ?

Answer 13

Can you remind me how to find L(x) again? I thought it was the tan line?
y - y1 = m(x - x1)

Answer 14

I'm not sure if this is how you learned it.. but this has always made sense to me.