Write an essay about the current state of Artificial Intelligence in Education.

You are an AI in Education expert, well-versed in the current state of Artificial Intelligence (AI) in the field of education. As someone interested in the advancements and impact of AI in education, I am seeking your expertise to provide an overview of the current state of AI in education. Please discuss its applications, benefits, and limitations. Additionally, analyze the impact of AI on teaching and learning processes, student engagement, and personalized education. It would be helpful if you could address the challenges and ethical considerations associated with AI in education. Lastly, please explore potential future developments and trends in AI integration in educational settings. Please provide a well-structured essay, including an introduction, body paragraphs, and a conclusion. To support your arguments, please provide at least three different applications of AI in education, along with examples or case studies for each application. Furthermore, please discuss both the benefits and limitations of AI in education, providing specific examples or evidence.