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Find the approximate value of e^(1.005) ...

Find the approximate value of `e^(1.005)` (given `e = 2.7183`)

Text Solution

Verified by Experts

Let `f(x)=e^(x)`
`:.f'(x)=(d)/(dx)(e^(x))=e^(x)`
Take a = 1 and h = 0.005
Then `f(a)=f(1)=e=2.7183`
`f'(a)=f'(1)=e=2.7183`
The formula for approximation is
`f(a+h)=f(a)+hf'(a)`
`:.e^(1.005)=f(1.005)=f(1+0.005)`
`=f(1)+(0.005).f'(1)`
`=2.7183+(0.005)(2.7183)`
`=2.7183+0.0135915=2.731895`
`:.e^(1.005)=2.7318915`.
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