Calculus

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Use linear approximation, i.e. the tangent line, to approximate (1/0.504) as follows: Find the equation of the tangent line to f(x)=1/x at a "nice" point near 0.504. Then use this to approximate (1/0.504).

  • Calculus -

    The idea behind the approximation is:

    y(x)=1/x
    y'(x)=-1/x²
    Let x=x0+Δx
    y(x) = y(x0)+y'(x0)*Δx
    =y(x)-Δx / (x0 ²)

    Now apply x0=0.5, Δx=0.004

    y(0.504)=y(0.5)-0.004/0.5²
    =2-0.016
    =1.984
    compare to approximate actual value of
    1.984126984126984

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