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Section 4-12 : Differentials

For problems 1 – 3 compute the differential of the given function.

  1. \(f\left( x \right) = {x^2} - \sec \left( x \right)\) Solution
  2. \(w = {{\bf{e}}^{{x^{\,4}} - {x^{\,2}} + 4x}}\) Solution
  3. \(h\left( z \right) = \ln \left( {2z} \right)\sin \left( {2z} \right)\) Solution
  4. Compute \(dy\) and \(\Delta y\) for \(y = {{\bf{e}}^{{x^{\,2}}}}\) as x changes from 3 to 3.01. Solution
  5. Compute \(dy\) and \(\Delta y\) for \(y = {x^5} - 2{x^3} + 7x\) as x changes from 6 to 5.9. Solution
  6. The sides of a cube are found to be 6 feet in length with a possible error of no more than 1.5 inches. What is the maximum possible error in the volume of the cube if we use this value of the length of the side to compute the volume? Solution