Q. Which of the following statements is true regarding the function f(x) = 1/(x-3)?
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A.
Continuous at x = 3
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B.
Discontinuous at x = 3
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C.
Continuous everywhere
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D.
Discontinuous everywhere
Solution
The function f(x) = 1/(x-3) is discontinuous at x = 3 because it is undefined at that point.
Correct Answer:
B
— Discontinuous at x = 3
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Q. Which of the following statements is true regarding the function f(x) = |x|?
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A.
Continuous everywhere
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B.
Discontinuous at x = 0
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C.
Continuous only for x > 0
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D.
Discontinuous for x < 0
Solution
The function f(x) = |x| is continuous everywhere, including at x = 0.
Correct Answer:
A
— Continuous everywhere
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Q. Which of the following vectors is orthogonal to the vector A = 2i + 3j?
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A.
3i - 2j
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B.
-3i + 2j
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C.
2i + 3j
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D.
i + j
Solution
A vector is orthogonal if A · B = 0. For B = 3i - 2j, A · B = 6 - 6 = 0.
Correct Answer:
A
— 3i - 2j
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