编写Java+Application,求出e=1+1+\div+1!+1+\div+2!+1+\div+3!++\dotsc+1/n!+\dotsc的近似值,要求误差小于0.00001。

首先，我们可以使用以下代码在Java中计算e的近似值，直到误差小于0.00001为止：

public class CalculateE {
    public static void main(String[] args) {
        double e = 1.0;
        double term = 1.0;
        int n = 1;

        while (term >= 0.00001) {
            term = term / n;
            e += term;
            n++;
        }

        System.out.println("e的近似值为: " + e);
    }
}

这段代码使用了一个循环来计算每个项的值，并将其累加到e中，直到最后一个项小于0.00001为止。输出的结果将是e的近似值。

回答完问题后，这里是您要求的相关问题：

相关问题：
1. 如何在Java中计算阶乘？
. 如何在Java中计算指数值？
3. 如何在Java中处理浮点数的精度问题？
4. 如何使用递归来计算e的近似值？
5. 如何优化计算e的近似值的性能？

相关问题

帮我用java+vue实现一个简单的图书管理系统

A：

首先，你可以使用Java编写后端，使用Vue编写前端。下面是一个示例：

1. 后端代码：

package com.example.library;

import org.springframework.boot.SpringApplication;
import org.springframework.boot.autoconfigure.SpringBootApplication;

@SpringBootApplication
public class LibraryApplication {

    public static void main(String[] args) {
        SpringApplication.run(LibraryApplication.class, args);
    }
}

package com.example.library.controller;

import com.example.library.entity.Book;
import com.example.library.service.BookService;
import org.springframework.beans.factory.annotation.Autowired;
import org.springframework.http.HttpStatus;
import org.springframework.http.ResponseEntity;
import org.springframework.web.bind.annotation.*;

import java.util.List;

@RestController
@RequestMapping("/api/v1/books")
public class BookController {

    @Autowired
    private BookService bookService;

    @GetMapping
    public ResponseEntity<List<Book>> getBooks() {
        List<Book> books = bookService.getBooks();
        return new ResponseEntity<>(books, HttpStatus.OK);
    }

    @PostMapping
    public ResponseEntity<Book> addBook(@RequestBody Book book) {
        Book addedBook = bookService.addBook(book);
        return new ResponseEntity<>(addedBook, HttpStatus.CREATED);
    }

    @PutMapping("/{id}")
    public ResponseEntity<Book> updateBook(@PathVariable Long id, @RequestBody Book book) {
        Book updatedBook = bookService.updateBook(id, book);
        return new ResponseEntity<>(updatedBook, HttpStatus.OK);
    }

    @DeleteMapping("/{id}")
    public ResponseEntity<Void> deleteBook(@PathVariable Long id) {
        bookService.deleteBook(id);
        return new ResponseEntity<>(HttpStatus.NO_CONTENT);
    }
}

package com.example.library.entity;

import lombok.AllArgsConstructor;
import lombok.Data;
import lombok.NoArgsConstructor;

import javax.persistence.*;

@Data
@AllArgsConstructor
@NoArgsConstructor
@Entity
@Table(name = "books")
public class Book {

    @Id
    @GeneratedValue(strategy = GenerationType.AUTO)
    private Long id;

    private String title;

    private String author;

    private String publisher;
}

package com.example.library.repository;

import com.example.library.entity.Book;
import org.springframework.data.jpa.repository.JpaRepository;

import java.util.Optional;

public interface BookRepository extends JpaRepository<Book, Long> {

    Optional<Book> findById(Long id);
}

package com.example.library.service;

import com.example.library.entity.Book;
import com.example.library.exception.ResourceNotFoundException;
import com.example.library.repository.BookRepository;
import org.springframework.beans.factory.annotation.Autowired;
import org.springframework.stereotype.Service;

import java.util.List;

@Service
public class BookService {

    @Autowired
    private BookRepository bookRepository;

    public List<Book> getBooks() {
        return bookRepository.findAll();
    }

    public Book addBook(Book book) {
        return bookRepository.save(book);
    }

    public Book updateBook(Long id, Book newBook) {
        Book oldBook = bookRepository.findById(id).orElseThrow(() -> new ResourceNotFoundException("Book not found"));
        oldBook.setTitle(newBook.getTitle());
        oldBook.setAuthor(newBook.getAuthor());
        oldBook.setPublisher(newBook.getPublisher());
        return bookRepository.save(oldBook);
    }

    public void deleteBook(Long id) {
        bookRepository.deleteById(id);
    }
}

2. 前端代码：

<template>
  <div>
    <table>
      <thead>
        <tr>
          <th>ID</th>
          <th>Title</th>
          <th>Author</th>
          <th>Publisher</th>
          <th>Actions</th>
        </tr>
      </thead>
      <tbody>
        <tr v-for="book in books" :key="book.id">
          <td>{{ book.id }}</td>
          <td>{{ book.title }}</td>
          <td>{{ book.author }}</td>
          <td>{{ book.publisher }}</td>
          <td>
            <button @click="editBook(book)">Edit</button>
            <button @click="deleteBook(book.id)">Delete</button>
          </td>
        </tr>
      </tbody>
    </table>
    <div v-if="showForm">
      <h2 v-if="!editMode">Add book</h2>
      <h2 v-if="editMode">Edit book</h2>
      <form @submit.prevent="submitForm">
        <label>Title:</label>
        <input type="text" v-model="book.title" required>
        <label>Author:</label>
        <input type="text" v-model="book.author" required>
        <label>Publisher:</label>
        <input type="text" v-model="book.publisher" required>
        <button type="submit">{{ editMode ? 'Save changes' : 'Add' }}</button>
      </form>
    </div>
    <button @click="showForm = true">Add book</button>
  </div>
</template>

<script>
import axios from 'axios';

export default {
  data() {
    return {
      books: [],
      showForm: false,
      editMode: false,
      book: {
        title: '',
        author: '',
        publisher: '',
      },
    };
  },
  created() {
    this.getBooks();
  },
  methods: {
    async getBooks() {
      const { data } = await axios.get('/api/v1/books');
      this.books = data;
    },
    async addBook(book) {
      await axios.post('/api/v1/books', book);
      this.getBooks();
    },
    async updateBook(id, book) {
      await axios.put(`/api/v1/books/${id}`, book);
      this.getBooks();
    },
    async deleteBook(id) {
      await axios.delete(`/api/v1/books/${id}`);
      this.getBooks();
    },
    editBook(book) {
      this.editMode = true;
      this.showForm = true;
      this.book = { ...book };
    },
    async submitForm() {
      if (this.editMode) {
        await this.updateBook(this.book.id, this.book);
      } else {
        await this.addBook(this.book);
      }
      this.showForm = false;
      this.editMode = false;
      this.book = {
        title: '',
        author: '',
        publisher: '',
      };
    },
  },
};
</script>

请注意，这只是一个简单的示例，可以根据您的需要进行更改和修改。您还需要相应配置您的数据库和后端框架以进行完整的实现。

使用springboot+mybatis+thymeleaf编写代码实现分页查询

首先，需要在pom.xml中引入相应的依赖，这里以MySQL数据库为例：

<!-- SpringBoot Web模块 -->
<dependency>
    <groupId>org.springframework.boot</groupId>
    <artifactId>spring-boot-starter-web</artifactId>
</dependency>

<!-- SpringBoot Mybatis模块 -->
<dependency>
    <groupId>org.mybatis.spring.boot</groupId>
    <artifactId>mybatis-spring-boot-starter</artifactId>
    <version>2.2.0</version>
</dependency>

<!-- MySQL驱动 -->
<dependency>
    <groupId>mysql</groupId>
    <artifactId>mysql-connector-java</artifactId>
    <version>8.0.23</version>
</dependency>

其次，需要配置Mybatis和数据库连接，可以在application.yml中配置：

spring:
  datasource:
    driver-class-name: com.mysql.cj.jdbc.Driver
    url: jdbc:mysql://localhost:3306/testdb?serverTimezone=UTC&useSSL=false&characterEncoding=utf8
    username: root
    password: root

mybatis:
  config-location: classpath:mybatis-config.xml
  mapper-locations: classpath:mapper/*.xml

其中，`datasource`为数据源的基本信息，`mybatis`则是Mybatis的配置信息，包括配置文件的位置和Mapper文件的位置。

接下来，需要编写Mapper接口和对应的Mapper XML文件。以User表为例：

public interface UserMapper {
    List<User> findUserByPage(@Param("start") Integer start, @Param("pageSize") Integer pageSize);
}

<mapper namespace="com.example.demo.mapper.UserMapper">
    <select id="findUserByPage" resultType="com.example.demo.entity.User">
        select * from user limit #{start},#{pageSize}
    </select>
</mapper>

其中，`findUserByPage`方法为分页查询方法，`start`为起始位置，`pageSize`为每页数量。

最后，编写Controller层和前端页面。以UserController为例：

@Controller
public class UserController {
    @Autowired
    private UserMapper userMapper;

    @GetMapping("/user")
    public String findUserByPage(@RequestParam(value = "pageNum", defaultValue = "1") Integer pageNum,
                                 @RequestParam(value = "pageSize", defaultValue = "5") Integer pageSize,
                                 Model model) {
        Integer start = (pageNum - 1) * pageSize;
        List<User> userList = userMapper.findUserByPage(start, pageSize);
        PageInfo pageInfo = new PageInfo(userList);
        model.addAttribute("pageInfo", pageInfo);
        return "user";
    }
}

其中，`findUserByPage`方法接收两个参数：`pageNum`和`pageSize`，表示当前页和每页数量。通过计算获得起始位置，调用Mapper接口进行分页查询，并通过`PageInfo`类将查询结果传递给前端页面。

在前端页面中通过`th:each`循环遍历查询结果，并通过`th:href`生成分页链接。以user.html为例：

<!DOCTYPE html>
<html lang="en" xmlns:th="http://www.thymeleaf.org">
<head>
    <meta charset="UTF-8">
    <title>User List</title>
</head>
<body>
<table border="1">
    <thead>
    <tr>
        <th>ID</th>
        <th>Name</th>
        <th>Age</th>
        <th>Gender</th>
    </tr>
    </thead>
    <tbody>
    <tr th:each="user : ${pageInfo.list}">
        <td th:text="${user.id}"></td>
        <td th:text="${user.name}"></td>
        <td th:text="${user.age}"></td>
        <td th:text="${user.gender}"></td>
    </tr>
    </tbody>
</table>
<div>
    <a th:href="@{/user?pageNum=1}">首页</a>
    <a th:href="@{/user?pageNum=${pageInfo.prePage}}">上一页</a>
    <a th:href="@{/user?pageNum=${pageInfo.nextPage}}">下一页</a>
    <a th:href="@{/user?pageNum=${pageInfo.pages}}">尾页</a>
</div>
</body>
</html>

其中，`pageInfo.list`为查询结果列表，通过`th:each`循环遍历生成表格数据。底部的分页链接则通过`th:href`生成相应的链接。

到这里，一个简单的分页查询就完成了。需要注意的是，以上代码仅为示例，具体实现方式可能会有所不同，需要按照实际需求进行调整。