Calculus Help
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MATH140Quiz2A.docxMATH 140 Quiz 2 NAME___________________________ Professor: Dr. J. Beyers
INSTRUCTIONS
· The quiz is worth 100 points. There are five problems (each worth 20 points).
· This quiz is open book and open notes . This means you may refer to your textbook, notes, and online classroom materials. You may take as much time as you wish, provided you turn in your quiz no later than the due date posted in our syllabus.
· You must show all work in order to receive full credit. If you do not show your work, you may earn only partial or no credit at the discretion of the professor.
· Emailed quizzes and exams will not be accepted (they crash my email system). Thank you for understanding.
· If you have any questions, please feel free to send me a PAGER message in LEO.
Best of luck!
MULTIPLE CHOICE Select the best answer choice. Write your answer choices below:
(1) _____
(2) _____
(3) _____
(4) Fill-in-the-blank (proof)
(5) _____
(1) _____ Evaluate the following limit
(A) 0
(B) 1/4
(C) 1/2
(D) 1
(E) None of the above
(2) _____ Use the graphs of and in Figure 1 and the Limit Principles to find the following limits provided they exist:
Figure 1
2
3
-3
-2
G(x)
F(x)
-1
-3
1
-2
3
2
-1
0
1
(A) 5 9 1 3
(B) 3 -4 4 1
(C) 0 9 does not exist 3
(D) 5 9 does not exist 3
(E) none of the above
(3) _____ Find the following limit, if it exists
(A) 0
(B) 1/4
(C) 1/2
(D) Does not exist
(E) None of the above
(4) Fill-in-the-blank: Use an method to prove the following limit
Note: Substituting into the expression to verify the limit, is not a proof using the method.
Proof: (Fill-in-the-blank)
Find a value for :
___________________________________________________________________
___________________________________________________________________
And since, _____________________________, we need to show for every , there exists a , such that:
_____________________________ ______________________________________
___________________________________________________________________
Suggesting a good candidate for would be: _______________________
Confirm that the value works:
To confirm the candidate is valid for a given , choose _______ and assume ______________ .
Then consider: _______________________________________________
Therefore, if ______________ _____, then _______________________
Which proves by definition our limit statement:
___________________________________________________________________
(5) _ ____ Find the equation of the tangent line to the curve at . Write your answer in slope-intercept form, .
(Note: You must use the definition of the slope of the tangent, no “short-cuts” yet.)
(A) (B) (C) (D) (E) None of the above
(6) Find the derivative: f(x) = 8 − 3x 2
For problem 6, perform these steps:
(a) Calculate and simplify:
msec =
(b) Determine mtan = msec
(c) Evaluate mtan at x = 2
(d) Find an equation of the line tangent to the graph of f at (2, f(2))
