Question

find the linear approximation of the fnct f(x)=sqrt(1-x) at a=0 and use it to approximate the numbers (sqrt0.9) and (sqrt0.99)

Answer 1

So do you know how to find the tangent line at x=0?

Answer 2

\[y=mx+b <--\text{ line} \]
m=f ' (x=a)=f ' (x=0)=f ' (0)
You need to find f ' (x).
Then evaluate f ' (x) at x=0.
y=f ' (0) x + b
We still need to find b though.
But we are given a point on this line (0,f(0))
What is f(0)?

We will plug in what we know to find what b is:
f(0)=f ' (0) * 0 +b
f(0)=b

SO great.We have the tangent line here at x=0 is
y=f ' (0) x + f(0)

Answer 3

Let me know when you find what f ' (0) and f(0) is, then I will give you further assistance.

Answer 4

i was showed some different L(x)= f(a)+f'(a)(x-a)