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Question
Find the approximate values of : e2.1, given that e2 = 7.389
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Solution
Let f(x) = ex
Then f'(x) = `d/dx(e^x) = e^x`
Take a = 2 and h = 0.1
Then f(a) = f(2) = e2 = 7.389
f'(a) = f'(2) = e2 = 7.389
The formula for approximation is
f(a + h) ≑ f(a) + h.f'(a)
∴ e2.1 = f(2.1)
= f(2 + 0.1)
≑ f(2) + (0.1).f'(2)
≑ 7.389 + 0.1 x 7.389
≑ 7.389 + 0.7389
= 8.1279
∴ e2.1 ≑ 8.1279.
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