explicit function

简明释义

显函数

英英释义

例句

1.In mathematics, an explicit function 显式函数 is defined by an equation that directly relates the output to the input.

在数学中，显式函数 explicit function 是通过一个方程直接将输出与输入相关联的。

2.In contrast, an implicit function may not provide a clear formula for y, unlike an explicit function 显式函数.

相比之下，隐式函数可能不会提供y的明确公式，这与显式函数 explicit function不同。

3.The derivative of an explicit function 显式函数 is straightforward to compute using standard rules.

使用标准规则计算显式函数 explicit function 的导数是简单明了的。

4.An explicit function 显式函数 can be easily graphed because you can find y for any given x.

因为您可以为任何给定的x找到y，所以显式函数 explicit function 可以很容易地绘制图形。

5.When programming, you often need to create an explicit function 显式函数 to perform a specific task.

在编程时，您通常需要创建一个显式函数 explicit function 来执行特定任务。

作文

In mathematics, the concept of an explicit function is crucial for understanding how different variables interact with each other. An explicit function is defined as a function in which the dependent variable is expressed directly in terms of the independent variable(s). This means that you can easily calculate the value of the dependent variable if you know the value of the independent variable. For example, in the equation y = 2x + 3, y is an explicit function of x. Here, you can see that for any value of x, you can directly compute the corresponding value of y without any ambiguity.The clarity provided by an explicit function makes it easier for mathematicians and scientists to analyze relationships between variables. It allows for straightforward calculations and predictions. In contrast, an implicit function is one where the relationship between the variables is not directly stated, making it more complex to derive the dependent variable from the independent variable. For instance, the equation x^2 + y^2 = 1 represents a circle, where y cannot be easily isolated as a function of x without further manipulation.Understanding explicit functions is not just limited to pure mathematics; it extends to various fields such as physics, economics, and engineering. For instance, in physics, the motion of an object can often be described using explicit functions. If we consider the equation of motion for a falling object under gravity, we might express the height h as a function of time t: h(t) = h0 - (1/2)gt^2, where h0 is the initial height and g is the acceleration due to gravity. Here, h is an explicit function of time t, allowing us to predict the height of the object at any given moment.In economics, explicit functions are used to model supply and demand. For example, a demand curve might be represented as Qd = a - bP, where Qd is the quantity demanded, P is the price, and a and b are constants. In this case, the quantity demanded is an explicit function of price, making it easy to determine how changes in price will affect demand.Moreover, the use of explicit functions simplifies the process of optimization. In calculus, finding the maximum or minimum values of a function often relies on the function being explicit. By taking derivatives and setting them to zero, we can find critical points that help identify optimal solutions. For example, if we have a profit function P(x) = 100x - x^2, where x is the number of units produced, we can easily differentiate this explicit function to find the production level that maximizes profit.In conclusion, mastering the concept of an explicit function is fundamental for anyone studying mathematics or related fields. It provides clarity and simplicity in expressing relationships between variables, facilitating analysis and problem-solving. Whether in theoretical contexts or practical applications, the role of explicit functions remains indispensable, enabling us to make sense of complex systems and make informed decisions based on mathematical reasoning. Understanding explicit functions not only enhances our mathematical skills but also enriches our ability to interpret and navigate the world around us.

在数学中，显式函数的概念对于理解不同变量之间的相互作用至关重要。显式函数被定义为一个函数，其中因变量直接以自变量的形式表达。这意味着如果你知道自变量的值，就可以轻松计算因变量的值。例如，在方程y = 2x + 3中，y是x的显式函数。在这里，你可以看到，对于任何x的值，你都可以直接计算出对应的y值，而没有任何歧义。显式函数所提供的清晰性使得数学家和科学家更容易分析变量之间的关系。它允许进行简单的计算和预测。相比之下，隐式函数是指变量之间的关系并未直接表述，这使得从自变量推导因变量变得更加复杂。例如，方程x^2 + y^2 = 1表示一个圆，在没有进一步操作的情况下，y无法轻易地被孤立为x的函数。理解显式函数不仅限于纯数学，它还扩展到物理学、经济学和工程等多个领域。例如，在物理学中，物体的运动通常可以使用显式函数来描述。如果我们考虑一个在重力作用下自由下落的物体的运动方程，我们可以将高度h表示为时间t的函数：h(t) = h0 - (1/2)gt^2，其中h0是初始高度，g是重力加速度。在这个例子中，h是时间t的显式函数，使我们能够预测物体在任何给定时刻的高度。在经济学中，显式函数用于建模供求关系。例如，一个需求曲线可以表示为Qd = a - bP，其中Qd是需求量，P是价格，a和b是常数。在这种情况下，需求量是价格的显式函数，使得确定价格变化如何影响需求变得简单。此外，显式函数的使用简化了优化过程。在微积分中，寻找函数的最大值或最小值通常依赖于该函数是显式的。通过求导并将其设置为零，我们可以找到关键点，从而帮助识别最佳解决方案。例如，如果我们有一个利润函数P(x) = 100x - x^2，其中x是生产的单位数量，我们可以轻松地对这个显式函数进行微分，以找到最大化利润的生产水平。总之，掌握显式函数的概念对于任何学习数学或相关领域的人来说都是基础。它在表达变量之间的关系时提供了清晰性和简单性，促进了分析和问题解决。无论是在理论背景还是实际应用中，显式函数的角色始终不可或缺，使我们能够理解复杂系统并基于数学推理做出明智的决策。理解显式函数不仅提升了我们的数学技能，还丰富了我们解读和驾驭周围世界的能力。