Spring 2025
Name of student:
Problem Score
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Calculators and any notes are NOT allowed during the exam. Any violations of the UCI Code
of Student Conduct will be reported. Please make sure that your answers are legible.
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, Problem 1. (20 points) True or false (No justification needed):
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(a) lim(x,y)→(0,0) xy sin x2 +y 2
does not exist.
(b) Two distinct lines in R3 either intersect at one point or are parallel.
(c) proj⃗a ⃗b is always parallel to ⃗a.
(d) There is a unique plane in R3 containing the points (1, 2, 1), (2, 3, 0), and (4, 5, −2).
(e) In polar coordinates, the point (r, θ) = (−100, π6 ) is the same as (r, θ) = (100, 7π
6
).
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