I. Functions, Graphs, and Limits

Analysis of graphs. With the aid of technology, graphs of functions are often

1.3 from the right; But we can use the special '−' or '+' signs (as shown) to define one sided limits: the left-hand limit (−) is 3.8; the right-hand limit (+) is 1.3; And the ordinary limit 'does not exist' Are limits only for difficult functions? Limits can be used even when we know the value when we get there! Nobody said they are only. In this introductory unit, students will explore the foundational aspects of calculus by learning the elementary concept of limits and discovering how limits relate to the continuity of functions. Students will be able to flow between the different representations of mathematics (i.e. Analytic, graphic, algebraic, and verbal) at any given time.

easy to produce. The emphasis is on the interplay between the geometric and

analytic information and on the use of calculus both to predict and to explain the

1.3 Limits Graphical And Analytical Connectionsap Calculus Answers

observed local and global behavior of a function.

Limits of functions (including one-sided limits)

• An intuitive understanding of the limiting process.

• Calculating limits using algebra.

• Estimating limits from graphs or tables of data.

Asymptotic and unbounded behavior

• Understanding asymptotes in terms of graphical behavior.•

Describing asymptotic behavior in terms of limits involving infinity.

• Comparing relative magnitudes of functions and their rates of change (for

example, contrasting exponential growth, polynomial growth, and logarithmic

growth).

Continuity as a property of functions

1.3 limits graphical and analytical connectionsap calculus solution

• An intuitive understanding of continuity. (The function values can be made as

close as desired by taking sufficiently close values of the domain.)

• Understanding continuity in terms of limits.

• Geometric understanding of graphs of continuous functions (Intermediate

1.3 Limits Graphical And Analytical Connectionsap Calculus Solution

Value Theorem and Extreme Value Theorem).