最常用的AP微积分词汇

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　　antiderivative 原函数a representation, usually in symbolic form, of any function whose derivative is a given function.

　　tangent 切线，斜率，正切a line or a plane that touches a curve or a surface at a single point.

　　chain rule 链式求导法the theorem that defines the method for taking the derivative of a composite function.

　　concave downward 向下开口part of a graph resembling an upside down bowl.

　　concave upward 向上开口part of a graph resembling a right side up bowl.

　　continuous 连续being in immediate connection or spatial relationship.

　　critical point 临界点point on the graph where the derivative is either 0 or undefined.

　　cylindrical shell method 旋转体积圆筒积分法technique for finding the volume of a solid of revolution.

　　definite integral 定积分the representation of the difference in values of a primitive of a given function evaluated at two designated points.

　　derivative 导数，求导，导函数the change of a function with respect to an infinitesimally small change in the independent variable, or the slope of the point's tangent line.

　　differentiable 可导的，可微的a function whose graph is curve that is smooth and contains no discontinuities or cusps.

　　disk method 旋转体积圆盘法technique for finding the volume of a solid of revolution when integrating along the axis of revolution.

　　extreme value theorem 极值理论guarantees an absolute max and an absolute min

　　first derivative test 极值点、拐点的确定法determines whether an inflection point is a minimum, maximum, or neither.

　　higher order derivatives 高阶导数，高阶导函数any derivatives beyond the first derivative.

　　implicit differentiation 隐函数求导、微分method for finding the derivative of an implicitly defined function or relation using the chain rule.

　　indefinite integral 不定积分another way of saying antiderivative.

　　instantaneous rate of change 瞬时牵连变化率、相关变化率rate of change at a particular moment.

　　instantaneous velocity 瞬时速度rate at which an object is moving at a particular moment.

　　integration by parts 分部积分a method of evaluating an integral by use of the formula, ∫udv = uv − ∫vdu.

　　limit 极限value that a function approaches as the domain variable approach a specific value.

　　mean value theorem 中值定理the theorem that there is a point in a continuous curve where the derivative is equal to the average derivative of the entire arc.

　　normal line 法线line that is at a 90 degree angle, perpendicular to a surface.

　　point-slope form 直线方程点斜式form used the most when finding the equation of a line.

　　riemann sum 黎曼积分method for approximating the definite integral.

　　second derivative test 用二阶导数检查是否是极大值点或极小值点determines whether a critical point is a relative minimum or maximum using the value of the second derivative at the point.

　　u-substitution U型变量代换integration method that involves using the chain rule in reverse.

　　trigonometric substitution 三角函数变量代换substitution of trigonometric functions for other expressions to eliminate radicals in integrals.

　　washer method 旋转体积的圆筒积分法similar to the disk method but using washers instead of disks.