Limits, Continuity and Local Linearity

In this limits worksheets, students graph tangent lines and determine the slope of a secant line. This one-page worksheet contains six multi-step problems.

One example is finding the limit as x approaches -1 of (2x+2)/(x+1), solved by simplifying the expression and then explored intuitively by looking at the left and right-hand limits. The second example of finding the limit as x approaches...

Determine how much a linear transformation alters area. The seventh segment in a series of 15 makes the connection between the determinant and the scale factor of areas during a linear transformation. The video goes on to explain the...

Take a different view at matrix multiplication. Based on vector transformations, the video presents matrix multiplication as the result of the composition of multiple linear transformations. The presentation explains the numerical...

How can you determine the rate of change on a curve? Pupils use the interactive to discover what happens with the average rate of change as the point move closer to the other. Using the definition of the derivative, learners find that it...

Push an engaging resource to the limit. The interactive allows learners to find a limit on quadratic functions graphically. Using sliders, pupils set the x-value for the limit and to move values from the left and right toward the limit.

What does it mean if young mathematicians cannot put the squeeze on a sequence? Learners investigate a divergent sequence and find the formula for the nth term. Using the definition of a limit of a sequence, pupils try to find the limit...

Limit the view of sequences on both sides of the axis. Learners explore an alternating sign sequence. Using a graphical display of the first 10 terms of the sequence, pupils determine the formula for the general term. they then use the...

Limits can provide some valuable information about graphs. A slider interactive lets learners see the behavior of a graph around asymptotes. They investigate relationships between limits and asymptotes.

Take a look at another alternating sequence. The resource provides a graphical display of a sequence that alternates between two values. Pupils use the display to determine whether the sequence has a limit. Given a theory of limit,...