MATH 2301-102 and -103 Fall 2017 Calculus I Recitation 7 Week 8

See the coversheet for instructions and the point value of each problem.

  1. Prove that \(\displaystyle \frac{d}{dx} \left(\cot^{-1}(x)\right) = -\frac{1}{1+x^2}\).
  2. A ladder \(10\,\mathrm{ft}\) long leans against a vertical wall. It starts slipping, and the bottom of the ladder slides away from the base of the wall at a speed of \(2\,\mathrm{ft/s}\).
    1. Draw and label a diagram illustrating this scenario.
    2. How fast is the angle between the ladder and the wall changing when the bottom of the ladder is \(6\,\mathrm{ft}\) from the base of the wall?
  3. Show that \(\displaystyle \cosh(x)-\sinh(x)=e^{-x}\).
  4. Use logarithmic differentiation to find the derivative of \[y=\left(\left(\tan^{-1}(\log_2(x))\right)^{\sinh(x^2)}\right)\csc(3^x) \,.\]

Last modified: Thu Oct 12 13:54:28 UTC 2017