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Optimizing JavaScript code for performance is crucial for delivering a smooth user experience. Techniques include minimizing HTTP requests by combining files, reducing DOM manipulation, using efficient data structures, and implementing code splitting to load only necessary scripts. Employing tools like browser developer tools and performance profilers can help identify bottlenecks and refine optimization strategies. These measures ensure your website runs swiftly and efficiently.

JavaScript offers numerous advantages for web development. Its dynamic nature allows for interactive elements like user interfaces, animations, and data validation. Its vast ecosystem of libraries and frameworks, such as React and Angular, simplifies complex tasks and fosters efficient development. Moreover, JavaScript's versatility extends to server-side programming with Node.js, enabling full-stack solutions. These factors contribute to JavaScript's widespread adoption as a foundational language for the modern web.

Memoization is a technique used in JavaScript to optimize code by storing the results of expensive function calls and returning the cached result when the same inputs occur again. This avoids redundant computations, significantly improving performance. For example, calculating the factorial of a number repeatedly benefits from memoization, as the results for each number can be stored and reused, eliminating the need to recalculate them.

To find the last entry in MongoDB, use the `sort()` method in conjunction with the `limit()` method. Sort your collection by the timestamp field in descending order and limit the result to 1 document. For example, `db.users.find().sort({timestamp: -1}).limit(1)` retrieves the document with the latest timestamp.

An API (Application Programming Interface) acts as a messenger between different software applications. It defines how these applications can interact and exchange data, just like a waiter takes your order from you and relays it to the kitchen. APIs specify the format of the data exchanged and the rules governing the interaction, allowing different systems to work together seamlessly.