Use linear Approximation to approximate e^.01

Question

Mathematics

Mateo Harding

19 May, 14:50

Use linear Approximation to approximate e^.01

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Answers (1)

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Zackary Arroyo · Answer 1

Suppose that:

let f (x) = e^x

Suppose:

a = 0

Now we are finding f (a):

f (a) = f (0) = 1

f ' (x) = e^x

Now we are finding f ' (a):

f ' (a) = f ' (0) = 1

Putting the formula:

L (x) = f (a) + f ' (a) (x - a)

L (e^0.01) = 1 + 1 (0.01 - 0)

= 1.01 is the answer