Pt1420 Unit 6 Study Guide

Name: __________________________ Date: _____________

1.|Complete the table and use the result to estimate the limit. x|||||||f(x)||||||||
A)|–0.076923|
B)|0.423077|
C)|0.298077|
D)|0.548077|
E)|–0.451923|

2.|Determine the following limit. (Hint: Use the graph of the function.)|
A)|6|
B)|5|
C)|1|
D)|4|
E)|does not exist|

3.|A graph of is shown and a c-value is given. For this problem, use the graph to find .|
A)|0|
B)|–10|
C)|–5|
D)|15|
E)|does not exist|

4.|Use the graph of and the given c-value to find .|
A)|–1|
B)|-6|
C)|3|
D)|–7|
E)|does not exist|

5.|Use properties of limits and algebraic methods to find the limit, if it exists.|
A)||
B)||
C)||
D)||
E)|does not exist|

6.|Find the
On the tangent line, P is the point of tangency and A is another point on the line. Use the coordinates of P and A to find the slope of the tangent line.|
A)|2|
B)|3|
C)|–1|
D)|–4|
E)|does not exist|

17.|Use the limit definition to find the slope of the tangent line to the graph of at the point .|
A)||
B)||
C)||
D)||
E)||

18.|Find the derivative of the following function using the limiting process.|
A)||
B)||
C)||
D)||
E)|none of the above|

19.|Find an equation of the a line that is tangent to the graph of f and parallel to the given line.|
A)||
B)||
when |
A)||
B)||
C)||
D)||
E)||

27.|The tangent line to a curve at a point closely approximates the curve near the point. In fact, for x-values close enough to the point of tangency, the function and its tangent line are virtually indistinguishable. This problem explores this relationship. Write the equation of the tangent line to the curve at the indicated point. To check your answer, use a graphing utility to graph both the function and its tangent line, and repeatedly zoom in on the point of tangency until the function and the tangent line cannot be distinguished.|
A)|43|
B)|3|
C)|4|
D)|46|
E)|6|

28.|Find the coordinates of points where the graph of f(x) has horizontal tangents. As a check, graph and see whether the points you found look as though they have horizontal tangents.|
A)||
B)||
C)||
D)||
E)||

29.|Find the average rate of change on the interval of the function .|
A)|–5|
B)|5|
C)|–1|
D)|11|
E)|–7|

30.|Suppose the height s (in feet) at time t (in seconds) of a silver dollar dropped from the top of the Washington Monument is given by . How long will it take the dollar to hit the ground? Round your answer to two decimal