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Key points of this exam paper are: Substituting, Function, Substituting Specific Values, Even Function, Graph, Axis, Information, Continuous, Properties, Separate Points
Typology: Exams
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October 5 Mathematics 105 Mr. Haines 2012 Calculus I Examination #
(5) I. Suppose the function f has rule
Prove that f is not an even function by substituting specific values for x.
(10) II. Graph ( )^ on your calculator.
A. Explain how you know from the graph of that the graph of is above the x-axis.
B. Explain how you know from the graph of that the graph of is below the x-axis.
(5) III. Suppose ( ) , ( ) , and ( ). Use this information to give a number that estimates ( ) :
(15) IV. Sketch below a graph of any function f whose graph contains the three separate points (1, 1), (3, 3), and (5, 5) and has all three of these properties:
A. f is not continuous at x = 5.
B. f does not have a limit at x = 1.
C. 3 is a stationary point but is not a local maximum or local minimum for.
(10) V. If possible, graph two distinct solutions to the differential equation. If not possible, explain why not.
(15) VIII. Suppose ( ) ( )( ).
A. Find all the stationary points of.
B. If ( )^ give a formula for ( ).
C. Find all of the local maximum values of on the interval [^ ].
D. Find all of the local minimum values of on the interval [ ].
E. Give the intervals where is decreasing.
(10) IX. If ( ) then
A. ( ) __________________________
B. Give the equation of the tangent line to the graph of ( ) at the point ( ( )).
(10) X. Suppose ( ) for all numbers x. Give a formula for ( ) if you know that ( ) and ( ).