Limits and continuity
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AP Calculus AB/BC - What Are Limits and Why Do They Matter?
This video introduces the concept of limits in calculus, explaining how they describe where a function approaches rather than where it is, using the example of (x²-9)/(x-3).
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AP Calculus AB/BC - Reading Limits from Graphs
Learn how to read limits from graphs by examining where y-values approach as x nears a target. Covers two-sided limits, discontinuities, and when limits don't exist.
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AP Calculus AB/BC - One-Sided Limits from Graphs
Explains one-sided limits: left-hand and right-hand approaches to a point. Shows that a two-sided limit exists only when both sides agree.
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AP Calculus AB/BC - Estimating Limits from Tables
Learn how to estimate limits using tables by approaching a point from both left and right sides, even when the function is undefined at that point.
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AP Calculus AB/BC - Limit Properties: Sums, Products, and Quotients
Learn how to break complex limits into smaller pieces using sum, difference, product, quotient, and constant rules to simplify calculations.
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AP Calculus AB/BC - Limits of Composite Functions
Learn how composite limits work: find the inner limit, verify continuity, then substitute. Includes step-by-step example with f(g(x)).
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AP Calculus AB/BC - Direct Substitution: The Easiest Way to Find Limits
Learn how to solve most AP Calculus limits in seconds using direct substitution for continuous functions. Covers polynomials, trig, exponentials, and when the method fails.
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AP Calculus AB/BC - Limits of Piecewise Functions
Learn how to evaluate limits of piecewise functions by checking left and right-hand limits separately at boundary points and comparing them.
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AP Calculus AB/BC - Finding Limits by Factoring
Learn how to find limits when direct substitution gives 0/0 by factoring and canceling. Example: lim(x→3) of (x²-9)/(x-3) using difference of squares.
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AP Calculus AB/BC - Finding Limits by Rationalizing (Conjugates)
Learn how to solve limits with square roots that result in 0/0 by multiplying by the conjugate. Example: lim(x→9) of (√x - 3)/(x - 9) = 1/6.
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AP Calculus AB/BC - Trig Limits Using Identities
Learn how to evaluate trigonometric limits using identities when direct substitution gives 0/0. Covers Pythagorean identities, factoring, and cancellation techniques.
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AP Calculus AB/BC - The Squeeze Theorem and Special Trig Limits
Learn the squeeze theorem and two essential trigonometric limits for AP Calculus: lim(x→0) sin(x)/x = 1 and lim(x→0) (1-cos(x))/x = 0.
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AP Calculus AB/BC - Continuity: Definition and Types of Discontinuities
Explains continuity in calculus and the three types of discontinuities: removable, jump, and infinite. Shows how limits and function values must match for continuity.
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AP Calculus AB/BC - Continuity of Piecewise Functions
Learn how to check if a piecewise function is continuous at a boundary point by verifying that the left limit, right limit, and function value all match.
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AP Calculus AB/BC - Removing Discontinuities
Learn how to remove removable discontinuities by finding limits and filling "holes" in functions, using factoring and simplification techniques.
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AP Calculus AB/BC - Infinite Limits and Vertical Asymptotes
This video explains vertical asymptotes in calculus, showing how functions behave when denominators approach zero and how to determine if limits go to positive or negative infinity.
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AP Calculus AB/BC - Limits at Infinity and Horizontal Asymptotes
Learn how to find horizontal asymptotes by comparing degrees and leading coefficients of rational functions, with clear examples and graphical visualization.
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AP Calculus AB/BC - Limits at Infinity with Square Roots
Learn how to evaluate limits at infinity involving square roots by dividing by the highest power and simplifying. Includes key tips on handling radicals and negative infinity.
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AP Calculus AB/BC - The Intermediate Value Theorem
Explains the Intermediate Value Theorem: continuous functions on closed intervals must pass through every value between their endpoints, with AP exam application steps.