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Calculus 1. A continuous function is function with no jumps, gaps, or undefined points.

A definite integral is defined as a limit of Riemann sums. The second derivative test method for determining a function's maxima, minima, and points of inflection by using its first and second derivatives. Functions (a) polynomials, rationals, exponentials, logarithmic, trigonometric, arctan, absolute value, radicals, power function i. graphs ii. A discontinuity is a point at which a function jumps suddenly in value, blows up, or is undefined. file: "https://calcworkshop.com/assets/captions/calculus-1.srt", //ga('send', 'event', 'Vimeo CDN Events', 'code', event.code);

If you're seeing this message, it means we're having trouble loading external resources on our website. The following video provides an outline of all the topics you would expect to see in a typical Single-Variable Calculus 1 class (i.e., Calculus 1, Business Calculus 1, AB Calculus, BC Calculus, or IB HL 2 Mathematics).. All of the topics are covered in detail in our Online Calculus 1 … Math.

An indefinite integral, also known as an antiderivative, is an integral without upper and lower limits. }); The chain rule is a formula for the derivative of the composition of two functions in terms of their derivatives.

//ga('send', 'event', 'Vimeo CDN Events', 'setupError', event.message); A Riemann sum is an estimate, using rectangles, of the area under a curve. Newton's method is an iterative method for numerically finding a root of a function. A limit is the value a function approaches as the variable approaches some point. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. });

Find out with our FREE Calculus Assessment Test.

file: "https://player.vimeo.com/external/140512144.m3u8?s=5d4dd81b08ef86dd08b8623c86beec90fe7eef3a", A critical point is a point in the graph of a function where the derivative is either zero or undefined. All of the topics are covered in detail in our Online Calculus 1 Course. aspectratio: "16:9", playerInstance.on('play', function(event) {

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continuity properties (b) inverse functions (c) composition of functions (d) functional notation (e) functions of two variables, i.e.

}] Donate or volunteer today! playerInstance.on('ready', function(event) { An integral is a mathematical object that can be interpreted as an area or a generalization of area. An inflection point is a point on a curve at which the concavity changes. Ready for Calculus? Khan Academy is a 501(c)(3) nonprofit organization. playerInstance.on('setupError', function(event) { jwplayer.key = "GK3IoJWyB+5MGDihnn39rdVrCEvn7bUqJoyVVw=="; },{ If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. Calculus is the branch of mathematics studying the rate of change of quantities (which can be interpreted as slopes of curves) and the length, area, and volume of objects.

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The minimum of a set, function, etc.

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The maximum of a set, function, etc. skin: "seven", Have a test coming up?

width: "100%", preload: "auto", //ga('send', 'event', 'Vimeo CDN Events', 'error', event.message); The Course challenge can help you understand what you need to review.

"default": true Calculus 1. }); corresponding MathWorld classroom page.

To learn more about a topic listed below, click the topic name to go to the corresponding MathWorld classroom page.

The opposite of continuity. is the largest value attained by that object. sources: [{ A derivative is the infinitesimal rate of change in a function with respect to one of its parameters. If the function is not continuous, the limit could be different from the value of the function at that point. }); The following sections provide links to our complete lessons on all Calculus 1 topics. Implicit differentiation is the procedure of differentiating an implicit equation (one which has not been explicitly solved for one of the variables) with respect to the desired variable, treating other variables as unspecified functions of it. var playerInstance = jwplayer('calculus-player'); Integrals and derivatives are the fundamental objects of calculus. kind: "captions",

The first derivative test is a method for determining the maximum and minimum values of a function using its first derivative. }]

is the smallest value attained by that object. tracks: [{

It includes 22 Questions to help you find your strengths and weaknesses prior to taking a calculus course. }], Test your knowledge of the skills in this course.

A definite integral is an integral with upper and lower limits.

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//ga('send', 'event', 'Vimeo CDN Events', 'FirstFrame', event.loadTime); Formal definition of limits (epsilon-delta), Derivative rules: constant, sum, difference, and constant multiple, Combining the power rule with other derivative rules, Derivatives of cos(x), sin(x), ˣ, and ln(x), Derivatives of tan(x), cot(x), sec(x), and csc(x), Implicit differentiation (advanced examples), Derivatives of inverse trigonometric functions, L’Hôpital’s rule: composite exponential functions, Extreme value theorem and critical points, Intervals on which a function is increasing or decreasing, Analyzing concavity and inflection points, Fundamental theorem of calculus and accumulation functions, Interpreting the behavior of accumulation functions, Fundamental theorem of calculus and definite integrals, Integrating using long division and completing the square, Integrating using trigonometric identities, Verifying solutions for differential equations, Particular solutions to differential equations, Area: curves that intersect at more than two points, Volume: squares and rectangles cross sections, Volume: triangles and semicircles cross sections, Volume: disc method (revolving around x- and y-axes), Volume: disc method (revolving around other axes), Volume: washer method (revolving around x- and y-axes), Volume: washer method (revolving around other axes). Calculus 1 Overview

The following video provides an outline of all the topics you would expect to see in a typical Single-Variable Calculus 1 class (i.e., Calculus 1, Business Calculus 1, AB Calculus, BC Calculus, or IB HL 2 Mathematics).

The fundamental theorems of calculus are deep results in analysis that express definite integrals of continuous functions in terms of antiderivatives. Calculus 1 Common Topics List1 1.

}); Topics in a Calculus I Course. jwplayer().setCurrentQuality(0);

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Our mission is to provide a free, world-class education to anyone, anywhere. The extreme value theorem states that a continuous function on a closed interval has both a maximum and minimum value. Course summary; Limits and continuity. //ga('send', 'event', 'Vimeo CDN Events', 'setupTime', event.setupTime);

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