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March 23, 2008

A particle moves along the curve y=\ln x so that its abscissa is increasing at a rate of 2 units per second. At what rate is the particle moving away from the origin as it passes through the point (e,1)?

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Normal Line Problem

March 23, 2008

Find the equation of the line normal to the curve \displaystyle y=\tanh \left[\sin^{-1} \left( x-\sqrt{2}\right) \right] at the point where \displaystyle x=\sqrt{2}.

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Derivatives of Integrals

March 5, 2008

Evaluate the following.

  1. \displaystyle \frac{d}{dx} \int_{x}^{0} \sqrt{1+t^{4}}\ dt
  2. \displaystyle \frac{d}{dx} \int_{\frac{1}{x}}^{\sqrt{x}} \cos t^{2}\ dt,\; x>0
  3. \displaystyle \frac{d^{2}}{dx^{2}} \int_{0}^{x} \left( \int_{1}^{\sin t} \sqrt{1+u^{4}}\ du \right) dt

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Posted by wMw