수학, 예술, 컴퓨터 프로그래밍, 경제, 물리학, 화학, 생물학, 의학, 금융, 역사 등을 무료로 학습하세요. Determining limits using algebraic properties of limits: limit properties, Determining limits using algebraic properties of limits: direct substitution, Determining limits using algebraic manipulation, Selecting procedures for determining limits, Determining limits using the squeeze theorem, Connecting infinite limits and vertical asymptotes, Connecting limits at infinity and horizontal asymptotes, Working with the intermediate value theorem, Defining average and instantaneous rates of change at a point, Defining the derivative of a function and using derivative notation, Estimating derivatives of a function at a point, Connecting differentiability and continuity: determining when derivatives do and do not exist, Derivative rules: constant, sum, difference, and constant multiple: introduction, Derivative rules: constant, sum, difference, and constant multiple: connecting with the power rule, Derivatives of cos(x), sin(x), ˣ, and ln(x), Finding the derivatives of tangent, cotangent, secant, and/or cosecant functions, Differentiating inverse trigonometric functions, Selecting procedures for calculating derivatives: strategy, Selecting procedures for calculating derivatives: multiple rules, Further practice connecting derivatives and limits, Interpreting the meaning of the derivative in context, Straight-line motion: connecting position, velocity, and acceleration, Rates of change in other applied contexts (non-motion problems), Approximating values of a function using local linearity and linearization, Using L’Hôpital’s rule for finding limits of indeterminate forms, Extreme value theorem, global versus local extrema, and critical points, Determining intervals on which a function is increasing or decreasing, Using the first derivative test to find relative (local) extrema, Using the candidates test to find absolute (global) extrema, Determining concavity of intervals and finding points of inflection: graphical, Determining concavity of intervals and finding points of inflection: algebraic, Using the second derivative test to find extrema, Sketching curves of functions and their derivatives, Connecting a function, its first derivative, and its second derivative, Exploring behaviors of implicit relations, Riemann sums, summation notation, and definite integral notation, The fundamental theorem of calculus and accumulation functions, Interpreting the behavior of accumulation functions involving area, Applying properties of definite integrals, The fundamental theorem of calculus and definite integrals, Finding antiderivatives and indefinite integrals: basic rules and notation: reverse power rule, Finding antiderivatives and indefinite integrals: basic rules and notation: common indefinite integrals, Finding antiderivatives and indefinite integrals: basic rules and notation: definite integrals, Integrating functions using long division and completing the square, Integrating using linear partial fractions, Modeling situations with differential equations, Verifying solutions for differential equations, Approximating solutions using Euler’s method, Finding general solutions using separation of variables, Finding particular solutions using initial conditions and separation of variables, Exponential models with differential equations, Logistic models with differential equations, Finding the average value of a function on an interval, Connecting position, velocity, and acceleration functions using integrals, Using accumulation functions and definite integrals in applied contexts, Finding the area between curves expressed as functions of x, Finding the area between curves expressed as functions of y, Finding the area between curves that intersect at more than two points, Volumes with cross sections: squares and rectangles, Volumes with cross sections: triangles and semicircles, Volume with disc method: revolving around x- or y-axis, Volume with disc method: revolving around other axes, Volume with washer method: revolving around x- or y-axis, Volume with washer method: revolving around other axes, The arc length of a smooth, planar curve and distance traveled, Defining and differentiating parametric equations, Second derivatives of parametric equations, Finding arc lengths of curves given by parametric equations, Defining and differentiating vector-valued functions, Solving motion problems using parametric and vector-valued functions, Defining polar coordinates and differentiating in polar form, Finding the area of a polar region or the area bounded by a single polar curve, Finding the area of the region bounded by two polar curves, Defining convergent and divergent infinite series, Determining absolute or conditional convergence, Finding Taylor polynomial approximations of functions, Radius and interval of convergence of power series, Finding Taylor or Maclaurin series for a function, See how our content aligns with AP®︎ Calculus BC standards. Learn AP® Calculus BC for free—everything from AP® Calculus AB plus a few extra goodies, such as Taylor series, to prepare you for the AP® test. AP® é uma marca comercial registrada da College Board, que não revisou este recurso. Finding the carrying capacity of a population that grows logistically. Korzystasz z Khan Academy w języku polskim? Partial sums: formula for nth term from partial sum | Series | AP Calculus BC | Khan Academy To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Przekaż 1% podatku lub darowiznę Fundacji Edukacja dla Przyszłości, która zajmuje się tłumaczeniem Khan Academy na język polski, edukacjaprzyszlosci.pl. Korzystasz z Khan Academy w języku polskim? AP® /College Calculus BC Unit: Limits and continuity 0 Legend (Opens a modal) Possible mastery points Skill Summary Legend (Opens a modal) About the course Learn Khan Academy in the classroom … Full curriculum of exercises and videos. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. AP® is a registered trademark of the College Board, which has not reviewed this resource. ¡Esta es una buena preparación para tu próximo examen! Khan Academy … AP® sınavı College Board kurumunun tescilli markasıdır ve College Board bu kaynağı kontrol etmemiştir. Khan Academy … Nuestra misión es proporcionar una educación gratuita de clase mundial para cualquier persona en cualquier lugar. Korzystasz z Khan Academy w języku polskim? AP® es una marca registrada de College Board, que no ha revisado este recurso. Sal interviews the AP Calculus Lead at College Board, Level up on the above skills and collect up to 700 Mastery points, Limits of combined functions: piecewise functions, Theorem for limits of composite functions, Theorem for limits of composite functions: when conditions aren't met, Limits of composite functions: internal limit doesn't exist, Limits of composite functions: external limit doesn't exist, Limits of combined functions: sums and differences, Limits of combined functions: products and quotients, Limits of piecewise functions: absolute value, Direct substitution with limits that don't exist, Conclusions from direct substitution (finding limits), Next steps after indeterminate form (finding limits), Worked example: Continuity at a point (graphical), Worked example: point where a function is continuous, Worked example: point where a function isn't continuous, Functions continuous at specific x-values, Removing discontinuities (rationalization), Level up on the above skills and collect up to 600 Mastery points, Analyzing unbounded limits: rational function, Analyzing unbounded limits: mixed function, Limits at infinity of quotients with square roots (odd power), Limits at infinity of quotients with square roots (even power), Limits at infinity of quotients with square roots, Level up on the above skills and collect up to 500 Mastery points, Worked example: using the intermediate value theorem, Justification with the intermediate value theorem: table, Justification with the intermediate value theorem: equation, Justification with the intermediate value theorem, Level up on the above skills and collect up to 200 Mastery points, Formal definition of limits Part 1: intuition review, Formal definition of limits Part 2: building the idea, Formal definition of limits Part 3: the definition, Formal definition of limits Part 4: using the definition. Phillips Academy was one of the first schools to teach AP®︎ nearly 60 years ago. Bill Scott uses Khan Academy to teach AP®︎ Calculus at Phillips Academy in Andover, Massachusetts, and he’s part of the teaching team that helped develop Khan Academy’s AP®︎ lessons. Nuestra misión es proporcionar una educación gratuita de clase mundial para cualquier persona en cualquier lugar. Observa la resolución de preguntas libres de exámenes anteriores AP Calculus. Determining limits using algebraic properties of limits: limit properties, Determining limits using algebraic properties of limits: direct substitution, Determining limits using algebraic manipulation, Selecting procedures for determining limits, Determining limits using the squeeze theorem, Connecting infinite limits and vertical asymptotes, Connecting limits at infinity and horizontal asymptotes, Working with the intermediate value theorem. 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