AP Calculus AB · Unit 1: Limits and Continuity
1.12 Confirming Continuity over an Interval
In short
The depth of understanding includes knowing the formal definition that a function is continuous on an interval if and only if it is continuous at every single point within that interval. Furthermore, you are explicitly required to know as a foundational fact that polynomial, rational, power, exponential, logarithmic, and trigonometric functions are inherently continuous at all points within their respective domains.
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How is Confirming Continuity over an Interval tested on the exam?
This topic is assessed by having you determine intervals of continuity for various functions. The suggested skill is 1.E (Implementing Mathematical Processes), meaning you should be able to apply appropriate mathematical rules or procedures to find these intervals, both with and without the use of technology. You must be careful to correctly identify the domains of the specified function families to state where they are continuous.
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Confirming Continuity over an Interval: common questions
What do you need to know about Confirming Continuity over an Interval for AP Calculus AB?
The depth of understanding includes knowing the formal definition that a function is continuous on an interval if and only if it is continuous at every single point within that interval. Furthermore, you are explicitly required to know as a foundational fact that polynomial, rational, power, exponential, logarithmic, and trigonometric functions are inherently continuous at all points within their respective domains.
How is Confirming Continuity over an Interval tested on the AP Calculus AB exam?
This topic is assessed by having you determine intervals of continuity for various functions. The suggested skill is 1.E (Implementing Mathematical Processes), meaning you should be able to apply appropriate mathematical rules or procedures to find these intervals, both with and without the use of technology.
Where does Confirming Continuity over an Interval fit in AP Calculus AB?
Confirming Continuity over an Interval is topic 1.12 in Unit 1: Limits and Continuity of AP Calculus AB.
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