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Question
Find the approximate values of : (3.97)4
Solution
Let f(x) = x4
Then f'(x) = `d/dx(x^4)` = 4x3
Take a = 4 and h = – 0.03.
Then f(a) = f(4) = (4)4 = 256 and
f'(a) = f'(4) = 4(4)3 = 256
The formula for approximation is
f(a + h) ≑ f(a) + h.f'(a)
∴ (3.97)4 = f(3.97) = f(4 – 00.03)
≑ f(4) – (0.03)f'(4)
≑ 256 – 0.03 x 256
≑ 256 – 7.68
= 248.32
∴ (3.97)4 ≑ 248.32.
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