mixed-review-on-limits-pt-ii-calculus-ab-bc-practice-examples-problems-1-6-limit

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In this example we go over the algebraic determination of limits. Examples include radicals, rational expressions, absolute value, one sided limits, squeeze theorem sandwich, and limits involving infinity.

The student will define and apply the properties of limits of functions. Limits will be

evaluated graphically and algebraically. This will include

a) limits of a constant;

b) limits of a sum, product, and quotient;

c) one-sided limits; and

d) limits at infinity, infinite limits, and non-existent limits. *

*AP Calculus BC will include l'Hopital's Rule, which will be used to find the limit of

functions whose limits yield the indeterminate forms: 0/0 and ∞/∞.

APC.3 The student will use limits to define continuity and determine where a function is

continuous or discontinuous. This will include

a) continuity in terms of limits;

b) continuity at a point and over a closed interval;

c) application of the Intermediate Value Theorem and the Extreme Value Theorem; and

d) geometric understanding and interpretation of continuity and discontinuity.

APC.4 The student will investigate asymptotic and unbounded behavior in functions. This will

include

a) describing and understanding asymptotes in terms of graphical behavior and limits

involving infinity; and

b) comparing relative magnitudes of functions and their rates of change.

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