![]() Reinforce your conclusion with a graph or with a table Apply Theorem 1.7 to conclude analytically thatĤ. (Make sure you use a g where the limit of g(x) CAN be evaluated using direct substitution!)ģ. If the limit can't be evaluated with direct substitution, find a function g that agrees with f for all x other than x = c Recognize which limits can be evaluated by direct substitution (Theorems 1.1 - 1.6)Ģ. If the limit of g(x) as x approaches c exists, then the limit of f(x) also exists andġ. Let c be a real number and let f(x) = g(x) for all x ≠ c in an open interval containing c. Theorem 1.7 - Functions That Agree at All but One Point: Let c be a real number in the domain of the given trig function Theorem 1.6 - Limits of Trigonometric Functions: Theorem 1.5 - The Limit of a Composite Function: ![]() The following limit is valid for all c if n is odd, and it is valid for c > 0 if n is even: Theorem 1.4 - The Limit of a Function Involving a Radical: If r is a rational function given by r(x) = p(x) / q(x) and c is a real number such that q(c) ≠ 0, then If p is a polynomial function and c is a real number, then Theorem 1.3 - Limits of Polynomial and Rational Functions: Let b and c be real numbers, let n be a positive integer, and let f and g be functions with the following limits: Let b and c be real numbers and let n be a positive integer If you want to review some of the previous concepts you have learned before, you can check out AP Calculus AB or Precalculus.Direct Substitution can be used to evaluate a limit at c - if the function is continuous at c What class should I take after AP Calculus BC?Īfter mastering AP Calc BC, your follow up course should be Calculus 2.So, you more than welcome to learn from both of our AP Calculus AB and AP Calculus BC courses. Your StudyPug subscription gives you unlimited access to all math help in all courses. I want to get a head start on my upcoming advanced placement calculus class, but I'm still not sure if I'm going to take Calculus AB or Calculus BC.To save your precious study time, you can skip, review and learn any materials anytime based on your needs. You can review any math help in all courses, including Precalculus and AP Calculus AB. Your StudyPug subscription gives you unlimited access to all math help across all courses. I am studying for my AP Calculus BC exam, but I want to review some of the basics first.8.16Approximating functions with Taylor polynomials and error bounds.8.14Functions expressed as power series.8.13Radius and interval of convergence with power series.8.12Absolute and conditional convergence.8.9Comparison and limit comparison test.8.4Convergence and divergence of geometric series.8.3Convergence and divergence of normal infinite series.7.1Introduction to differential equations. ![]() 6.7Arc length and surface area of parametric equations.6.6Volumes of solids of revolution - Shell method.6.5Volumes of solids of revolution - Disc method. ![]()
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