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find a linearization function and approximate a. sqrt(25.07) and b. sqrt(24.96) the...

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barce90 | Student, Undergraduate | Honors

Posted May 15, 2013 at 4:45 AM via web

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find a linearization function and approximate a. sqrt(25.07) and b. sqrt(24.96) the linearization function is= a. the approximation of sqrt(25.07) is= b. the approximation sqrt(24.96) is=

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crmhaske | College Teacher | (Level 3) Associate Educator

Posted May 16, 2013 at 12:11 AM (Answer #1)

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A linearization function is defined as follows:

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

Where a is the whole number of x.

We know that:

`f(x) = sqrt(a)` and therefore:

`f'(x)=1/(2sqrt(a))`

Consequently, the linearization function is:

`f(x)=sqrt(a)+(x-a)/(2sqrt(a))`

For 25.07, x=25.07 and a=25:

`f(25.07)=sqrt(25)+(25.07-25)/(2sqrt(25))=5.007`

Therefore, the linear approximation of the square root of 25.07 is 5.007.

For 24.96, x=24.96 and a=24:

`f(24.96)=sqrt(24)+(24.96-24)/(2sqrt(24))=4.997`

Therefore, the linear approximation of the square root of 24.96 is 4.997.

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