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Giới hạn Practice Questions

THPT (Vietnam) · THPT Toán · 139 free MCQs with instant results and detailed explanations.

139
Total
43
Easy
69
Medium
27
Hard

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Sample Questions from Giới hạn

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Q1
Easy
What is the limit of the function f(x) = 3x + 2 as x approaches 5?
A. 17
B. 15
C. 20
D. 12
Show Answer & Explanation
Correct Answer: A
To find the limit of f(x) as x approaches 5, we simply substitute 5 into the function: f(5) = 3(5) + 2 = 15 + 2 = 17. Thus, the limit is 17.
Q2
Easy
If the limit of f(x) as x approaches 0 is 4, what can be concluded about the value of f(0)?
A. f(0) is equal to 4.
B. f(0) may or may not be 4.
C. f(0) is undefined.
D. f(0) must be greater than 4.
Show Answer & Explanation
Correct Answer: B
The limit of f(x) approaching 0 being 4 indicates that as x gets very close to 0, f(x) approaches 4. However, it does not provide information about the actual value of f(0), which could be different or undefined.
Q3
Easy
Evaluate the limit: lim(x→0) (sin(x)/x). What is the result?
A. 1
B. 0
C. ∞
D. 2
Show Answer & Explanation
Correct Answer: A
The limit of sin(x)/x as x approaches 0 is a well-known limit in calculus that equals 1.
Q4
Medium
Evaluate the limit: lim (x -> infinity) (5x^2 + 3)/(2x^2 - 7).
A. 5/2
B. 0
C. 1
D. 10
Show Answer & Explanation
Correct Answer: A
As x approaches infinity, the highest power terms dominate. The limit simplifies to the ratio of the leading coefficients: 5/2.
Q5
Medium
Find the limit of lim x->0 (sin(5x)/x).
A. 0
B. 1
C. 5
D. undefined
Show Answer & Explanation
Correct Answer: C
Using the limit property, lim x->0 (sin(kx)/x) = k. Here, k = 5, hence the limit is 5.
Q6
Medium
Evaluate the limit: lim x->infinity (2x^3 - 3x^2)/(x^3 + x + 1).
A. 2
B. 1
C. 0
D. infinity
Show Answer & Explanation
Correct Answer: A
When dividing the numerator and denominator by x^3, the dominant terms remain. Thus, the limit evaluates to 2/1 = 2.
Q7
Medium
What is the limit of f(x) = (x^2 - 4)/(x - 2) as x approaches 2?
A. 0
B. 2
C. 4
D. undefined
Show Answer & Explanation
Correct Answer: C
The function can be factored to (x + 2)(x - 2)/(x - 2), and after canceling (x - 2), the limit becomes 4 as x approaches 2.
Q8
Hard
Determine the limit: lim (x -> ∞) (3x^2 + 4x)/(2x^2 - x + 1).
A. 3/2
B. 2/3
C. 1
D. ∞
Show Answer & Explanation
Correct Answer: A
To find the limit as x approaches infinity, divide all terms by x^2, simplifying the rational function to (3 + 4/x)/(2 - 1/x + 1/x^2), and as x approaches infinity, the terms with x in the denominator approach 0, leaving the limit as 3/2.
Q9
Hard
Find the limit: lim(x→∞) [(3x^2 - 4x + 1) / (5x^2 + 2)].
A. 3/5
B. 1
C. 0
D. Infinity
Show Answer & Explanation
Correct Answer: A
As x approaches infinity, we focus on the leading terms of the numerator and denominator, which are 3x^2 and 5x^2 respectively. The limit can be simplified to (3/5), as the lower order terms become negligible.
Q10
Hard
Determine the limit: lim (x->∞) [(3x^2 + 5)/(2x^2 - 4x + 1)].
A. 3/2
B. 1
C. 0
D. ∞
Show Answer & Explanation
Correct Answer: A
For large values of x, the leading terms dominate. This simplifies to lim (x->∞) [(3x^2)/(2x^2)] = 3/2 as x approaches infinity.

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Giới hạn — THPT (Vietnam) THPT Toán Practice Questions Online

This page contains 139 practice MCQs for the chapter Giới hạn in THPT (Vietnam) THPT Toán. The questions are organized by difficulty — 43 easy, 69 medium, 27 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit.