Throughout this module, if something does not exist, write DNE in the answer box.

Recap Video

Take a look at the following video which recaps the ideas from the section.

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Example Video

Below are two videos showing worked examples.

Problems

Consider the limit This represents a definite integral for some function .
  • The function .
  • Evaluate the definite integral using geometry.
    Remember that if a graph goes below the -axis, the contribution to the definite integral is negative.

Consider a function whose graph is shown below.
PIC
Evaluate:
  • .
  • .
  • .
  • .
    Use the property .
  • .
    Use the property .

Consider on the interval .
  • The maximum and minimum values of on are, respectively, and .
  • Using the property described in the theorem, we can say

Suppose . Then
  • .
  • .
  • .

Consider the graph of below.
PIC
Let for .
  • The value of .
  • The value of .
  • The value of .
  • On which interval in is increasing? In interval notation: .
  • On which interval in is decreasing? In interval notation: .
  • The point is a local maximumminimum of .