Exploring Limits and Continuity in AP Calculus: A Comprehensive Guide
This guide covers key concepts in AP Calculus related to calculating limits, ensuring function continuity, and understanding vertical asymptotes. Learn how to determine limits for functions f(x) and g(x), find values for k to ensure that f(x) is continuous at specified points, and apply the Intermediate Value Theorem to find specific values within a defined interval. Additionally, the guide details the epsilon-delta definition of limits and provides visual examples to reinforce each concept.
Exploring Limits and Continuity in AP Calculus: A Comprehensive Guide
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Presentation Transcript
limits review AP Calculus
Calculate each limit: If f(x) =
Calculate the limit: g(x) = =
Given: f(x) = Solve for k such that f is continuous.
Sketch a graph that is discontinuous at x = 3, but approaches a limit of 5 as x approaches 3. Sketch a function f such that and
INTERMEDIATE VALUE THEOREM Given find the value of x in the interval [4, 7] guaranteed by the Intermediate Value Theorem such that y = 10. Round to the nearest thousandth.
Epsilon-Delta If h(x) =2 limit, L, of h as x approaches 2. Now find such that if , h is within units of L as x approaches 2.
