LIM-1.C.2 Graphical information about a function can be used to estimate limits. LIM-1.C.1 The concept of a limit includes one sided limits. _ 1.3 Estimating Limit Values from Graphs LIM-1.B.1 A limit can be expressed in multiple ways, including graphically, numerically, and analytically.ĭeltas and Epsilons Why this topic is not tested on the AP Calculus Exams. If the limit exists and is a real number, then LIM-1.A.1 Given a function f, the limit of f (x) as x approaches c is a real number R if f (x) can be made arbitrarily close to R by taking x sufficiently close to c (but not equal to c). IM-1.B Interpret limits expressed in analytic notation. LIM-1.A Represent limits analytically using correct notation. _ 1.2 Defining Limits Using Limit Notation LIM-1 Reasoning with definitions, theorems, and properties can be used to justify claims about limits.ġ.1 Introducing Calculus: Can change occur in an instant?ĬHA-1.A Interpret the rate of change at an instant in terms of average rates of change over intervals containing that instant.ĬHA-1.A.1 Calculus uses limits to understand and model dynamic change.ĬHA-1.A.2 Because an average rate of change divides the change in one variable by the change in another, the average rate of change is undefined at a point where the change in the independent variable would be zero.ĬHA-1.A.3 The limit concept allows us to define instantaneous rate of change in terms of average rates of change.
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