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- Mathematics
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- University Of Johannesburg (UJ)
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Math 124 Final Examination Autumn 2022Your Name Your Signature
Student ID # Quiz Section
Professor’s Name TA’s Name
READ THE INSTRUCTIONS!
• These exams will be scanned. Write you name, student number and quiz section clearly.
• Turn off and stow away all cell phones, smart watches, mp3 players, and other similar devices.
No earbuds/headphones allowed during the exam.
• This exam is closed book. You may use one 8.5′′ × 11′′ sheet of handwritten notes (both sides
OK). Do not share notes. No photocopied or printed materials are allowed.
π √
• Give your answers in exact form unless instructed otherwise. For example, or 5 3 are exact
3
numbers while 1.047 and 8.66 are decimal approximations for the same numbers.
• You can only use a Texas Instruments TI-30X IIS calculator.
• In order to receive credit, you must show all of your work. If you do not indicate the way
in which you solved a problem, you may get little or no credit for it, even if your answer is
correct.
• This exam has 11 pages plus this cover page with 8 questions. Please make sure that your
exam is complete.
Problem Score Problem Score Problem Score
1 (14 pts) 4 (12 pts) 7 (11 pts)
2 (15 pts) 5 (11 pts) 8 (15 pts)
3 ( 12 pts) 6 (10 pts) Total
, Math 124, Autumn 2022 Final Examination Page 1 of 11
1. (14 total points) Determine each of the following limits. If there is no finite limit, write ∞,
−∞, or DNE (does not exist), whichever applies.
cos(3x) − 1
(a) (5 points) lim
x→0 x2
ex + e−x
(b) (4 points) lim+
x→0 ex − e−x
(c) (5 points) lim (ln(2x + 1) − ln(x + 1))
x→∞
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