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Question
Find the approximate values of : `sqrt(8.95)`
Solution
Let f(x) = `sqrt(x)`.
Then f'(x) = `(1)/(2sqrt(x)`.
Take a = 9 and h = – 0.05.
Then f(a) = f(9) = `sqrt(9)` = 3 and
f'(a) = f'(9) = `(1)/(2sqrt(9)) = (1)/(6)`.
The formula for approximation is
f(a + h) ≑ f(a) + h.f'(a)
∴ `sqrt(8.95)` = f(9 – 0.05)
≑ f(9) – (0.05)f'(9)
≑ `3 - 0.05 xx (1)/(6)`
≑ 3 – 0.0083 = 2.9917
∴ `sqrt(8.95)` ≑ 2.9917.
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