Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.
Trending News
Math Homework Help!!?
(1) Find the linear approximation of f (x) = sqrt(x) at x = 9.
(2) use your answer from part 1 to estimate sqrt(9.3).
3 Answers
- cidyahLv 73 years ago
1)
sqrt(9)=3
2)
f(x)=sqrt(x)
f'(x) = 1/(2sqrt(x))
f'(9) = 1/(2sqrt(9)) = 1/(2*3) = 1/6
f(9.3) = f(9) + (9.3-9)f'(9)
sqrt(9.3) = sqrt(9) + (0.3)(1/6)
sqrt(9.3) = 3 + 0.05
= 3.05
- Mike GLv 73 years ago
Point is (9,3)
f'(x) = 1/(2√x)
f'(9) = 1/6
Equation
y-3 = (1/6)(x-9)
y = x/6 + 3/2
f(x) = x/6 + 1.5
f(9.3) = 3.05
∴ √9.3 ≈ 3.05
- TomVLv 73 years ago
f(a) ≈ f(x) - f'(x)(x-a)
f(x) = √x
f'(x) = 1/(2√x)
(1) At x = 9
f(a) ≈ 3 - (9-a)/6 = (9+a)/6
(2) f(9.3) = √9.3 ≈ (9+9.3)/6 = 18.3/6 = 3.05
==============================================
Percent Error:
100%(3.05/√9.3 -1) ≈ 0.013%
(Quite a good approximation for practical engineering applications. By calculator √9.3 = 3.04959 to 5 decimal places)
