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Calculus: Limits of Functions Classroom ActivitiesDownload

### Limits of Indeterminant Forms

In this activity, students will graph f(x)=sin(x)/x in order to visually determine the limit as x approaches zero. They will confirm the answer numerically by tracing left and right limit points on a graph and looking at values in a table.
• TI-84 Plus CE
• TI-84 Plus C Silver Edition
• TI-84 Plus Silver Edition
• TI-84 Plus
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### Making Limits Exist

In this activity, students will graph piecewise functions and evaluate numerically and graphically the left hand limit and the right hand limit of the function as x approaches a given number, c.
• TI-84 Plus CE
• TI-84 Plus C Silver Edition
• TI-84 Plus Silver Edition
• TI-84 Plus
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### Graphical Consequences of Continuity

Students explore the graphical and numeric consequences of continuity.
• TI-84 Plus CE
• TI-84 Plus C Silver Edition
• TI-84 Plus Silver Edition
• TI-84 Plus
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### To Infinity and Beyond!

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Students' develop an understanding of what it means to take a limit at infinity. They learn to estimate limits from graphs and tables of values.
• TI-84 Plus CE
• TI-84 Plus C Silver Edition
• TI-84 Plus Silver Edition
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### Approaching Limits

In this activity, students' will investigate, both graphically and numerically, the limit of a function at a point. They will examine how a function behaves as the input approaches a particular value. They will estimate limits from graphs, and tables of values.
• TI-84 Plus CE
• TI-84 Plus C Silver Edition
• TI-84 Plus Silver Edition
• TI-84 Plus
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### Average Rate of Change, Difference Quotients, and Approximate Instantaneous Rate of Change.

In this activity, the average rate of change between two points is defined and then used as a concept connecting ideas of slope, difference quotients, and approximations of instantaneous rate of change.
• TI-84 Plus CE
• TI-84 Plus C Silver Edition
• TI-84 Plus Silver Edition
• TI-84 Plus
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### Is There a Limit to Which Side You Can Take?

In this activity, students will investigate the given function, and state and explain the limit at a particular value. They also state and explain the limit at a particular value from a graph.
• TI-84 Plus CE
• TI-84 Plus C Silver Edition
• TI-84 Plus Silver Edition
• TI-84 Plus
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### Graph of Functions and Their Derivatives

In this activity, students observe the derivative as an indicator of increasing/decreasing function behavior. They also see that the derivative is an indicator of local maxima/ minima function behavior. Students learn to associate the graph of a function with its derivative.
• TI-84 Plus CE
• TI-84 Plus C Silver Edition
• TI-84 Plus Silver Edition
• TI-84 Plus
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### Local Linearity, Differentiability and Limits of Difference Quotients

In this activity, students explore a graphical feature of some functions called local linearity. They also investigate the link between local linearity and differentiability through several examples.
• TI-84 Plus CE
• TI-84 Plus C Silver Edition
• TI-84 Plus Silver Edition
• TI-84 Plus
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