Use linear approximation to approximate 1 <mrow

syaoronsangelhwc17

syaoronsangelhwc17

Answered question

2022-05-09

Use linear approximation to approximate 1 / 0.254.

Answer & Explanation

Haylie Cherry

Haylie Cherry

Beginner2022-05-10Added 17 answers

Let's consider the function f ( x ) = 1 x . We can find the tangent line L ( x ) of f at x = 1 4 , and then evaluate L ( .254 ) to obtain our linear approximation.
See if you can find L ( x ) and finish the proof.
Jayden Mckay

Jayden Mckay

Beginner2022-05-11Added 3 answers

f ( x ) f ( a ) + f ( a ) ( x a )
with f ( x ) = 1 / x.
Since we know 1 / 0.25 = 4, let's use that and center our approximation at a = 0.25. Now f ( x ) = 1 / x 2 . At a = 1 / 4, we have that f ( a ) = 16. Therefore:
1 x 4 16 ( x 0.25 )
Now since x = 0.254, we get:
1 0.254 4 16 ( 0.254 0.25 )
1 0.254 4 16 ( 0.004 )
1 0.254 4 0.064 = 3.936
Note that the exact value is about 3.93700787402, so our estimate is pretty close

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