n.微积分

原形：calculus复数：calculuses

**Calculus is the branch of mathematics that deals with derivatives and integrals, helping us understand rates of change and accumulation.**
微积分是数学的一个分支，涉及导数和积分，帮助我们理解变化率和累积量。
**The derivative of a function at a point gives us the slope of the tangent line at that point.**
函数在某一点的导数给出了该点切线的斜率。
**Integration can be used to find the area under a curve or the volume of a solid of revolution.**
积分可以用来求曲线下的面积或旋转体的体积。
**L'Hôpital's rule is applied when evaluating limits involving indeterminate forms like 0/0 or ∞/∞.**
洛必达法则用于求解涉及不定型（如0/0或∞/∞）的极限问题。
**A Taylor series represents a function as an infinite sum of terms calculated from its derivatives at a single point.**
泰勒级数将函数表示为以该函数在一个点上的导数组成的无限项和。
**The fundamental theorem of calculus links differentiation and integration, stating that differentiation is the reverse process of integration.**
微积分基本定理建立了微分与积分之间的联系，说明微分是积分的逆过程。
**The mean value theorem guarantees that a continuous function on a closed interval has at least one point where its derivative equals its average rate of change.**
均值定理保证了一个在闭区间上连续的函数至少有一点，其导数等于它的平均变化率。
**Euler's method is a numerical technique for approximating solutions to differential equations by using linear approximations.**
欧拉方法是一种数值技术，通过使用线性近似来近似微分方程的解。
**A limit describes the behavior of a function as its input approaches a certain value.**
极限描述了当函数的输入接近某个特定值时函数的行为。
**Partial derivatives are used in multivariable calculus to find the rate of change of a function with respect to one variable, while keeping the other variables constant.**
偏导数在多元微积分中用于找到函数相对于一个变量的变化率，同时保持其他变量不变。