Ground Rules for Final Quiz
Sample Math 126 Final Quiz
Name: ____________________________________ 8-digit Pin: _____________
Instructors Name: __________________________ Section #: ______________
Date: _____________________________________ Time: _________________
Instructions:
Enter all information requested above. You can use any books, notes, calculator, and Mathematica, but there is no collaborating.
In the questions below, whenever the constants [pic] appear, replace them in turn with the numbers from your 8-digit pin above. For example, if your pin is 52637481 then replace [pic] with 5, [pic] with 2, [pic] with 6, etc. Write your answer on this exam sheet in the place marked “Answer:” after each question. Show your work for partial credit.
1. What is the value of [pic]?
Answer:__________________________
2. Simplify the expression [pic].
Answer:_________________________________
3. After replacing [pic] and [pic] from your pin, put the following sentence into mathematical form:
“The distance between the real numbers [pic] and [pic] is less than [pic].”
Answer:__________________________________________________________
4. After replacing [pic] from your pin, if [pic] determine the limits on the expression [pic] so that it is equivalent.
Answer: [pic]
Note: questions 5 and 6 are related:
5. After replacing [pic], [pic], and [pic] from your pin, expand the polynomial [pic] about the number [pic].
Answer:_____________________________________________________________
6. What is the equation of the tangent line to the polynomial in question #5 at the location on the polynomial where [pic]? What is the slope of the polynomial at [pic]?
Answer: [pic]__________________________ [pic]_____________________
7. After replacing [pic], [pic], and [pic] from your pin, give a sketch, by hand, of the implicitly- defined function [pic]. Label all intercepts.
[pic]
8. Give an equation of a polynomial that has one local-only maxima and one local-only minima. (Note: the polynomial may have other turning points that do not conflict with the given conditions.)
Answer: Equation: ______________________________________
9. After replacing [pic] and [pic] from your pin, give a sketch, by hand, of the rational function [pic]. Find the equations of: (1) any vertical asymptotes and (2) the polynomial asymptotic behavior as [pic]. Label all intercepts.
[pic]
Answer: Equations of Vertical Asymptotes: ____________________________________
Answer: Equation of Polynomial Asymptote as [pic]: _________________________
10. After replacing [pic] from your pin, find the area of the largest rectangle that has its base on the y-axis and its other two vertices lying on the parabola [pic] in the right half- plane, [pic]. Show your work.
Answer: [pic]__________
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