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Question
Find the approximate values of (4.01)3
Solution
Let f(x) = x3
Then, f'(x) = 3x2
Take a = 4 and h = 0.01
Then f(a) = f(4) = 43 = 64
and f'(a) = f'(4) = 3 × 42 = 48
The formula for approximation is
f(a + h) ≑ f(a) + h.f'(a)
∴ (4.01)3 = f(4 + 0.01)
≑ f(4) + (0.01) f'(4)
≑ 64 + 0.01 × 48
≑ 64 + 0.48
= 64.48
∴ (4.01)3 ≑ 64.48
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