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CALCULUS (9TH EDITION) BY JAMES STEWART EXAM QUESTIONS 2026 EXAM LATEST
VERSION SOLVED QUESTIONS & ANSWERS VERIFIED 100 %
Calculus (9th Edition) by James Stewart — Questions
CHAPTER 1: FUNCTIONS AND LIMITS (Q1–Q25)
1. Which of the following represents a function?
A) y² = x
B) x² + y² = 1
C) y = √(x)
D) x = y²
Correct Answer: C
Rationale: A function assigns exactly one output to each input. y = √(x) is a function
because each x ≥ 0 gives one nonnegative y. y² = x and x = y² are not functions (two y-
values for some x). x² + y² = 1 is a circle, not a function .
2. The domain of f(x) = 1/(x² − 4) is:
A) All real numbers
B) All real numbers except x = 2
C) All real numbers except x = ±2
D) x > 2
Correct Answer: C
Rationale: The denominator is zero when x² − 4 = 0, i.e., x = ±2. These values must be
excluded from the domain.
3. If f(x) = 2x² − 3x + 1, find f(−2).
A) 3
B) 15
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C) −3
D) 11
Correct Answer: B
Rationale: f(−2) = 2(4) − 3(−2) + 1 = 8 + 6 + 1 = 15.
4. The range of f(x) = x² + 1 is:
A) [1, ∞)
B) (−∞, 1]
C) [0, ∞)
D) All real numbers
Correct Answer: A
Rationale: Since x² ≥ 0, x² + 1 ≥ 1. The minimum value is 1 at x = 0, so the range is [1, ∞).
5. Which of the following is an exponential function?
A) f(x) = x³
B) f(x) = 3ˣ
C) f(x) = x^(1/2)
D) f(x) = log₂ x
Correct Answer: B
Rationale: An exponential function has the form f(x) = aˣ where a > 0 and a ≠ 1. f(x) = 3ˣ
is exponential .
6. limₓ→₂ (x² − 4)/(x − 2) =
A) 0
B) 2
C) 4
D) Does not exist
Correct Answer: C
Rationale: Factor: (x² − 4)/(x − 2) = (x − 2)(x + 2)/(x − 2) = x + 2 for x ≠ 2. As x → 2, x + 2 → 4 .
7. limₓ→₀ sin(x)/x =
A) 0
B) 1
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C) ∞
D) Does not exist
Correct Answer: B
Rationale: This is a fundamental trigonometric limit. limₓ→₀ sin(x)/x = 1.
8. A function f is continuous at x = a if:
A) f(a) exists
B) limₓ→ₐ f(x) exists
C) limₓ→ₐ f(x) = f(a)
D) f is differentiable at a
Correct Answer: C
Rationale: Continuity requires three conditions: f(a) is defined, the limit exists, and the
limit equals the function value .
9. The slope of the tangent line to y = x² at x = 3 is:
A) 3
B) 6
C) 9
D) 12
Correct Answer: B
Rationale: The derivative of x² is 2x. At x = 3, the slope is 2(3) = 6.
10. limₓ→∞ 1/x =
A) 0
B) 1
C) ∞
D) Does not exist
Correct Answer: A
Rationale: As x increases without bound, 1/x approaches 0.
11. Which of the following is a one-sided limit notation?
A) limₓ→ₐ f(x)
B) limₓ→ₐ⁻ f(x)
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C) limₓ→ₐ⁺ f(x)
D) Both B and C
Correct Answer: D
Rationale: limₓ→ₐ⁻ f(x) is the limit from the left, and limₓ→ₐ⁺ f(x) is the limit from the right.
Both are one-sided limits.
12. limₓ→₀ (1 − cos x)/x =
A) 0
B) 1
C) 1/2
D) ∞
Correct Answer: A
Rationale: Using the trigonometric identity or l'Hôpital's Rule, limₓ→₀ (1 − cos x)/x = 0.
13. The instantaneous velocity is defined as:
A) The slope of the secant line
B) The limit of average velocity as time interval approaches zero
C) The average rate of change
D) The total distance divided by total time
Correct Answer: B
Rationale: Instantaneous velocity is the limit of the average velocity as the time interval
approaches zero .
14. If f(x) = |x|, then f is:
A) Continuous everywhere but not differentiable at x = 0
B) Differentiable everywhere
C) Not continuous at x = 0
D) Differentiable at x = 0
Correct Answer: A
Rationale: |x| is continuous everywhere, but the derivative does not exist at x = 0
because the left and right derivatives differ.
15. limₓ→₃ (2x + 1) =
CALCULUS (9TH EDITION) BY JAMES STEWART EXAM QUESTIONS 2026 EXAM LATEST
VERSION SOLVED QUESTIONS & ANSWERS VERIFIED 100 %
Calculus (9th Edition) by James Stewart — Questions
CHAPTER 1: FUNCTIONS AND LIMITS (Q1–Q25)
1. Which of the following represents a function?
A) y² = x
B) x² + y² = 1
C) y = √(x)
D) x = y²
Correct Answer: C
Rationale: A function assigns exactly one output to each input. y = √(x) is a function
because each x ≥ 0 gives one nonnegative y. y² = x and x = y² are not functions (two y-
values for some x). x² + y² = 1 is a circle, not a function .
2. The domain of f(x) = 1/(x² − 4) is:
A) All real numbers
B) All real numbers except x = 2
C) All real numbers except x = ±2
D) x > 2
Correct Answer: C
Rationale: The denominator is zero when x² − 4 = 0, i.e., x = ±2. These values must be
excluded from the domain.
3. If f(x) = 2x² − 3x + 1, find f(−2).
A) 3
B) 15
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C) −3
D) 11
Correct Answer: B
Rationale: f(−2) = 2(4) − 3(−2) + 1 = 8 + 6 + 1 = 15.
4. The range of f(x) = x² + 1 is:
A) [1, ∞)
B) (−∞, 1]
C) [0, ∞)
D) All real numbers
Correct Answer: A
Rationale: Since x² ≥ 0, x² + 1 ≥ 1. The minimum value is 1 at x = 0, so the range is [1, ∞).
5. Which of the following is an exponential function?
A) f(x) = x³
B) f(x) = 3ˣ
C) f(x) = x^(1/2)
D) f(x) = log₂ x
Correct Answer: B
Rationale: An exponential function has the form f(x) = aˣ where a > 0 and a ≠ 1. f(x) = 3ˣ
is exponential .
6. limₓ→₂ (x² − 4)/(x − 2) =
A) 0
B) 2
C) 4
D) Does not exist
Correct Answer: C
Rationale: Factor: (x² − 4)/(x − 2) = (x − 2)(x + 2)/(x − 2) = x + 2 for x ≠ 2. As x → 2, x + 2 → 4 .
7. limₓ→₀ sin(x)/x =
A) 0
B) 1
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C) ∞
D) Does not exist
Correct Answer: B
Rationale: This is a fundamental trigonometric limit. limₓ→₀ sin(x)/x = 1.
8. A function f is continuous at x = a if:
A) f(a) exists
B) limₓ→ₐ f(x) exists
C) limₓ→ₐ f(x) = f(a)
D) f is differentiable at a
Correct Answer: C
Rationale: Continuity requires three conditions: f(a) is defined, the limit exists, and the
limit equals the function value .
9. The slope of the tangent line to y = x² at x = 3 is:
A) 3
B) 6
C) 9
D) 12
Correct Answer: B
Rationale: The derivative of x² is 2x. At x = 3, the slope is 2(3) = 6.
10. limₓ→∞ 1/x =
A) 0
B) 1
C) ∞
D) Does not exist
Correct Answer: A
Rationale: As x increases without bound, 1/x approaches 0.
11. Which of the following is a one-sided limit notation?
A) limₓ→ₐ f(x)
B) limₓ→ₐ⁻ f(x)
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C) limₓ→ₐ⁺ f(x)
D) Both B and C
Correct Answer: D
Rationale: limₓ→ₐ⁻ f(x) is the limit from the left, and limₓ→ₐ⁺ f(x) is the limit from the right.
Both are one-sided limits.
12. limₓ→₀ (1 − cos x)/x =
A) 0
B) 1
C) 1/2
D) ∞
Correct Answer: A
Rationale: Using the trigonometric identity or l'Hôpital's Rule, limₓ→₀ (1 − cos x)/x = 0.
13. The instantaneous velocity is defined as:
A) The slope of the secant line
B) The limit of average velocity as time interval approaches zero
C) The average rate of change
D) The total distance divided by total time
Correct Answer: B
Rationale: Instantaneous velocity is the limit of the average velocity as the time interval
approaches zero .
14. If f(x) = |x|, then f is:
A) Continuous everywhere but not differentiable at x = 0
B) Differentiable everywhere
C) Not continuous at x = 0
D) Differentiable at x = 0
Correct Answer: A
Rationale: |x| is continuous everywhere, but the derivative does not exist at x = 0
because the left and right derivatives differ.
15. limₓ→₃ (2x + 1) =
