Tìm tất cả các giá trị của tham số \(m\) để đồ thị hàm số \(y=\frac{2 x+1}{\sqrt{m x^{2}+1}}\) có hai đường tiệm cận ngang.
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Nếu \(m=0\) thì hàm số trở thành hàm số bậc nhất nên không có tiệm cận.
Nếu \(m>0\) thì mẫu số dương và tập xác định của hàm số là \(D=\mathbb{R}\).
Ta có \(\lim _{x \rightarrow \pm \infty} \frac{2 x+1}{\sqrt{m x^{2}+1}}=\lim _{x \rightarrow \pm \infty} \frac{x\left(2+\frac{1}{x}\right)}{|x| \sqrt{m+\frac{1}{x}}}= \pm \frac{2}{\sqrt{m}}\).
Khi đó với \(m>0\) thì đồ thị hàm số có hai đường tiệm cận ngang \(y= \pm \frac{2}{\sqrt{m}}\).
Nếu \(m<0\) hàm số có tập xác định là \(D=\left(-\frac{1}{\sqrt{-m}}; \frac{1}{\sqrt{-m}}\right)\) nên đồ thị hàm số không có tiệm cận ngang mà chỉ có hai tiệm cận đứng là \(x= \pm \frac{1}{\sqrt{-m}}\).
Vậy \(m>0\) thỏa mãn yêu cầu bài toán.
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Read the following passage about endangered languages and mark the letter A, B, C or D on your answer sheet to indicate the best answer to each of the following questionsfrom 31 to 40.
[I] Social media has become a dominant force in modern communication, offering a range of benefits and challenges. [II] It has revolutionized the way people interact, share information, and even form relationships. [III] While these platforms offer opportunities for connection and expression, they also have their drawbacks. [IV] For instance, excessive use of social media has been linked to a range of negative effects, including mental health issues, social isolation, and decreased productivity. [V] However, when used responsibly, social media can also offer a variety of positive outcomes, such as the ability to stay connected with loved ones, network professionally, and access valuable information and resources.
One of the major benefits of social media is its ability to keep people connected. For example, individuals who live far apart can maintain close relationships through regular communication on these platforms. Social media also facilitates professional networking, allowing users to connect with potential employers or clients, and enabling companies to promote their products and services to a global audience. Additionally, platforms like Facebook, Twitter, and Instagram provide a space for people to share ideas, opinions, and creative work, fostering a sense of community and collaboration.
Despite these advantages, there are serious concerns about the negative impact of social media, particularly on mental health. Studies have shown that excessive social media use can contribute to feelings of anxiety, depression, and loneliness. This is often attributed to the unrealistic portrayals of life that are commonly shared on these platforms, leading to comparisons that can make individuals feel inadequate or left out. Furthermore, constant exposure to negative news or online bullying can exacerbate these feelings and contribute to long-term psychological stress.
Another issue with social media is its potential to distract people from their daily responsibilities. With notifications constantly popping up and endless streams of content to scroll through, individuals may find it difficult to focus on tasks such as work, school, or personal obligations. This can result in decreased productivity and a lack of attention to important matters.
Ultimately, the impact of social media depends on how it is used. If individuals are mindful of their usage patterns and take steps to limit their time on these platforms, they can enjoy the benefits of staying connected and informed without the negative consequences. Parents, educators, and mental health professionals can also play a role in helping young people develop healthy habits and manage their social media use effectively.
What can be inferred from the passage?
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Cho mệnh đề sau:
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Read the passage below and choose A, B, C or D.
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What is the word “potentially” in paragraph 4 closest in meaning to?
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Read the following asvertisment and mark the leeter A, B, C and D on your answer sheer to indeicate the option that best fit each of the numbered blanks from 1 to 6.
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Dựa vào bản đồ dưới đây (Atlat Địa lí Việt Nam, Nxb Giáo dục Việt Nam, 2024) và kiến thức đã học, trả lời câu hỏi dưới đây:
Chế độ nhiệt nước ta có sự phân hóa đa dạng do tác động chủ yếu của
Hoạt động phân chia các yếu tố sản xuất cho các ngành sản xuất, các đơn vị sản xuất khác nhau để tạo ra sản phầm được gọi là gì?