**1**Relate the derivative to everyday problems.**1.1**Identify everyday situations of quantitative and constant change.**1.2**Identify situations of variation related to time.**1.3**Determine constant changes in functions of a real variable.**1.4**Model situations of variation through functions of a real variable.**1.5**Identify the derivative as an instantaneous rate of change.**1.6**Interpret the derivative as an instantaneous velocity.**1.7**Interpret the second derivative as an acceleration.**1.8**Solve optimization problems using derivatives.**1.9**Explain solutions to rate of change and optimization problems, through geometric models.

**2**Use L`Hopital`s rule to calculate limits.**2.1**Use a change of variables in limits at zero and infinity.**2.2**Determine the convergence of the numerator and denominator of a rational function.**2.3**Identify derivable functions in a rational function.**2.4**Find the nth derivative of a function of a real variable.**2.5**Identify rational functions of 0/0 and infinite/infinite forms.**2.6**Use L`Hopital`s Rule to find the convergence of limits.**2.7**Practice the use of as, than, that with concepts from the studied topics.

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