Exam 2 Study Guide

  • high school geometry
  • area of rectangle
  • area of circle
  • surface area of sphere
  • volume of sphere
  • volume of cone
  • volume of box or cube
  • Chapters 1 and 2 as covered in the Exam 1 Study Guide.
  • Chapter 3
  • definitions
  • e
  • loga u, ln u
  • sin u, cos u, tan u
  • sin-1 u, cos-1 u, tan-1 u
  • sinh u, cosh u, tanh u
  • sinh-1 u, cosh-1 u, tanh-1 u
  • derivatives (with proofs) of the following types of expressions:
  • c, x, cu, u+v, u-v, uv, 1/v, u/v
  • un, eu, au, uv
  • composite functions, inverse functions
  • loga u, ln u
  • sin u, cos u, tan u
  • sin-1 u, cos-1 u, tan-1 u
  • sinh u, cosh u, tanh u
  • sinh-1 u, cosh-1 u, tanh-1 u
  • identities:
  • cos2 u + sin2 u = 1
  • cosh2 u - sinh2 u = 1
  • 1 + tan2 u = sec2 u
  • 1 - tanh2 u = sech2 u
  • reading graphs
  • recognizing limits as derivatives
  • computing certain limits by rewriting them in terms of derivatives
  • equations of tangent lines and normal lines
  • implicit differentiation
  • logarithmic differentiation
  • rates of change of quantities with units, in physics, economics, or the social sciences; for example: velocity, population growth, etc.
  • higher derivatives; for example: acceleration, jerk.