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Question
Find the approximate values of : 32.01, given that log 3 = 1.0986
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Solution
Let f(x) = 3x
Then f'(x) = `d/dx(3^x) = 3^x.log3`
Take a = 2 and h = 0.01
Then f(a) = f(2) = 32 = 9
and f'(a) = f'(2) = 32.log3
= 9 x 1.0986
= 9.8874
The formula for approximation is
f(a + h) ≑ f(a) + h.f'(a)
∴ 32.01 = f(2.01)
= f(2 + 0.01)
≑ f(2) + (0.01).f'(2)
≑ 9 + 0.01 x 9.8874
≑ 9 + 0.098874
= 9.098874
∴ 32.01 ≑ 9.098874.
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