Q. What is the slope of the tangent line to the curve y = x^2 at the point (1,1)? (2023)
Solution
The derivative y' = 2x; At x = 1, slope = 2(1) = 2.
Correct Answer:
B
— 2
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Q. What is the slope of the tangent line to the curve y = x^2 at the point (2, 4)?
Solution
The derivative y' = 2x. At x = 2, the slope is y'(2) = 2(2) = 4.
Correct Answer:
A
— 2
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Q. What is the slope of the tangent line to the curve y = x^2 at the point (3, 9)? (2020)
Solution
The derivative y' = 2x. At x = 3, y' = 2(3) = 6.
Correct Answer:
B
— 6
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Q. What is the slope of the tangent line to the curve y = x^3 at x = 1? (2019)
Solution
The derivative y' = 3x^2. At x = 1, y' = 3(1^2) = 3.
Correct Answer:
C
— 3
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Q. What is the value of the derivative of f(x) = 3x^3 - 2x at x = 1?
Solution
f'(x) = 9x^2 - 2. At x = 1, f'(1) = 9*1^2 - 2 = 7.
Correct Answer:
A
— 7
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Q. Which of the following functions is continuous at all points?
-
A.
f(x) = 1/x
-
B.
f(x) = x^3
-
C.
f(x) = sqrt(x)
-
D.
f(x) = tan(x)
Solution
f(x) = x^3 is a polynomial function, which is continuous everywhere.
Correct Answer:
B
— f(x) = x^3
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Q. Which of the following functions is continuous at x = 0?
-
A.
f(x) = 1/x
-
B.
f(x) = e^x
-
C.
f(x) = tan(x)
-
D.
f(x) = 1/(x^2 + 1)
Solution
The function f(x) = e^x is continuous everywhere, including at x = 0.
Correct Answer:
B
— f(x) = e^x
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Q. Which of the following functions is continuous on the interval [0, 1]?
-
A.
f(x) = 1/x
-
B.
f(x) = x^3
-
C.
f(x) = sqrt(x)
-
D.
f(x) = 1/(x-1)
Solution
f(x) = x^3 is a polynomial function and is continuous on the interval [0, 1].
Correct Answer:
B
— f(x) = x^3
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Q. Which of the following statements is true about the function f(x) = 1/(x-1)? (2022)
-
A.
Continuous at x = 1
-
B.
Continuous everywhere
-
C.
Not continuous at x = 1
-
D.
Continuous at x = 0
Solution
The function f(x) = 1/(x-1) is not continuous at x = 1 because it is undefined there.
Correct Answer:
C
— Not continuous at x = 1
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Q. Which of the following statements is true about the function f(x) = 1/(x-3)?
-
A.
Continuous at x = 3
-
B.
Continuous everywhere
-
C.
Not continuous at x = 3
-
D.
Continuous at x = 0
Solution
The function f(x) = 1/(x-3) is not defined at x = 3, hence it is not continuous at that point.
Correct Answer:
C
— Not continuous at x = 3
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Q. Which of the following statements is true about the function f(x) = |x|?
-
A.
Continuous everywhere
-
B.
Discontinuous at x = 0
-
C.
Continuous only at x = 1
-
D.
Discontinuous everywhere
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 statements is true regarding the function f(x) = 1/(x-3)?
-
A.
Continuous at x = 3
-
B.
Discontinuous at x = 3
-
C.
Continuous everywhere
-
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|?
-
A.
Continuous everywhere
-
B.
Discontinuous at x = 0
-
C.
Continuous only for x > 0
-
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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