CUNY Lehman College Algebra Worksheet

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Math181 Final Exam-Morning.pdf
Math 181 Final Exam – Morning Version
Directions: All answers must be given in exact form (in terms of or including radicals) unless
otherwise stated in the problem. All work must be shown for an answer to receive full credit. If
you have any questions about the test, please ask in Zoom text chat or use the Raise Hand
reaction to be moved into a breakout room. When finished, scan your work as a PDF and
attach it to the Blackboard assignment to submit your work no later than 1:05pm. Good luck!
1. Find each of the following limits analytically, using the properties of limits and algebraic
techniques, or explain why they do not exist. Non-algebraic solutions will not be
accepted.
5t-7
a. lim
t-11²-4
x²-6x+8
b. lim
x-2x²-5x+6
3x³-5x²+1
x-00 2x³+x-4
c. lim
d. lim xe-*
x →∞0
2. Find the derivative of each of the following functions. Simplify each derivative as much
as possible.
a. k(x) =
LTE
3x²
(x²+1)³
b. g(x) = (2x²7x)6(x² + 4x −9)
c. h(x) = x¹e2x+5
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Math181 Final Exam-Morning.pdf
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b. g(x) = (2x²7x)6(x² + 4x −9)
c. h(x) = x¹e2x+5
d. f(x) = 2 tan¹x + ln (1+x²)
3. Use the limit definition of the derivative to find the derivative of f(x) = x² + 3x.
4. Find the second derivative of f(x) = √√x³ + √√x²
LTE
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Math181 Final Exam-Morning.pdf
4 of 9 :he second derivative of f(x) = √√x³ +√x²
5. Find for the equation x²y – 3y² = 10.
dx
6. Find the absolute extrema of g(x) = cos x – x on the interval [0,2π].
LTE
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Math181 Final Exam-Morning.pdf
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LTE
13. The owner of a small farm wants to fence off a rectangular field that is bordered on one
side by a creek for grazing animals. The farmer has 2000 feet of fencing available with
which to surround the remaining three sides of the field. What are the dimensions of
the field with the greatest area that can be surrounded in this way? What is the area of
this largest field?
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