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Chapter 2 Test Study Guide
Limits and Continuity
For the test you will need to know how to do the following. Make sure to show all steps leading to your
answers, including any intermediate results obtained using a graphing calculator.
1. Use graphs to estimate the limits and value of the function, or explain why the limits do not
exist.
2. Determine the limit by substitution.
3. Find the limit of an arbitrary function graphically. Show how the Sandwich Theorem can be used
to confirm your answer.
4. For any function, use graphs and tables to find the limit as x goes to positive and negative
infinity. Determine the equation of horizontal asymptotes
5. Find the vertical asymptotes of the graph of an arbitrary function. Describe the behavior of f(x)
to the left and right of each vertical asymptote.
6. For any function find a simple basic function right end behavior model, and a simple basic
function left end behavior model.
7. Find the point(s) of discontinuity of a function. For each discontinuity, identify the type of
discontinuity.
8.
Determine the value of a function that would make it be continuous at a hole.
9. Sketch a possible graph for a function f, given information about limits and continuity at certain
points.
10. Find the average rate of change of the function over a closed interval.
11. For an arbitrary function determine, the slope of the curve at a point, an equation of the
tangent line, an equation of the normal line.