Tri asked in Science & MathematicsPhysics · 9 years ago

If v(t)=d'(t) is the instantaneous rate of change of d(t) at time t, then lim v(t)=? when t-->infinity?

d(t)= √((2 – 2t)^2 + (3t)^2)

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  • 9 years ago
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    d(t) = √((2 - 2∙t)² + (3∙t)²)

    = √(4 - 8∙t + 4∙t² + 9∙t²)

    = √(13∙t² - 8∙t + 4)

    using chain rule you can find the velocity:

    v(t) = d' = (13∙t² - 8∙t + 4)' ∙ (1/2) ∙ [1/√(13∙t² - 8∙t + 4)]

    = (26∙t - 8) ∙ (1/2) ∙ [1/√(13∙t² - 8∙t + 4)]

    = (13∙t - 4)/√(13∙t² - 8∙t + 4)

    lim|t→∞| v(t)

    = lim|t→∞| (13∙t - 4)/√(13∙t² - 8∙t + 4)

    >divide by numerator and denominator by t

    = lim|t→∞| (13 - 4/t)/√(13 - 8/t + 4/t²)

    = (13 - 0)/√(13 - 0 + 0)

    = √13

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