Calculus

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Use the Linear Approximation to estimate ∆f=f(3.5)−f(3) for f(x)=2/(1+x^(2))?
Δf ≈


Estimate the actual change.

(Use decimal notation. Give your answer to five decimal places.)
Δf=

Compute the error and the percentage error in the Linear Approximation.

(Use decimal notation. Give your answer to five decimal places.)

Error =

  • Calculus -

    linear approximation means get the slope.

    df/dx=-2(2x)/(1+x^2)^2

    at at x=3.25, df/dt= -4*3.25/(1+3.25^2)^2=-.0972

    df=-.0972*x but x= 3.5-3=.5
    df=-.0488
    actual

    f(3)=2/(10)=1/5
    f(3.5)=2/(1+3.5^2)=.150
    f(3.5-f(3)=-.050

    error (.0488-.050)/.050 about 2 percent
    f(3.5)-f(3)=-.350

  • Calculus -

    it says the answer is incorrect

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