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Question
Find the approximate values of : e0.995, given that e = 2.7183.
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Solution
Let f(x) = ex.
Then f'(x) = `d/dx(e^x) = e^x`
Take a = 1 and h = – 0.005.
Then f(a) = f(1) = e = 2.7183
and f'(a) = f'(1) = e = 2.7183
The formula for approximation is
f(a + h) ≑ f(a) + h.f'(a)
∴ e.0995 = f(0.995)
= f(1 – 0.005)
≑ f(1) – (0.005).f'(1)
≑ 2.7183 – 0.005 x 2.7183
≑ 2.7183 – 0.01359
= 2.70471
∴ e0.995 ≑ 2.70471.
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