See the coversheet for instructions and the point value of each problem.
-
Prove that \(\displaystyle \frac{d}{dx} \left(\cot^{-1}(x)\right)
= -\frac{1}{1+x^2}\).
- 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 \(2\,\mathrm{ft/s}\).
- Draw and label a diagram illustrating this
scenario.
- 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?
-
Show that \(\displaystyle \cosh(x)-\sinh(x)=e^{-x}\).
- 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