Calculus
Change Motion and Limits flashcards
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- What does “Average Rate of Change” mean?Average Versus Instantaneous Change
- The ratio of output change to input change across an interval.
- What important condition applies to average rate of change?Average Versus Instantaneous Change
- A secant rate summarizes an interval, not necessarily an instant.
- What does “Instantaneous Rate” mean?Average Versus Instantaneous Change
- A derivative measuring change at a single input.
- What important condition applies to instantaneous rate?Average Versus Instantaneous Change
- Speed is |velocity|, not always velocity itself.
- What does “Graphical Limit Evidence” mean?Limits from Graphs and Tables
- Interpreting a limit from the stated two-sided behavior of a graph.
- What important condition applies to graphical limit evidence?Limits from Graphs and Tables
- A filled point shows a value, not necessarily the limit.
- What does “Table Evidence and a Known Rule” mean?Limits from Graphs and Tables
- Using nearby table values together with a stated rule to evaluate a limit.
- What important condition applies to table evidence and a known rule?Limits from Graphs and Tables
- A finite table alone cannot prove every limit claim.
- What does “Limits at Holes” mean?Limits from Graphs and Tables
- A finite limit determined despite an undefined value at the target input.
- What important condition applies to limits at holes?Limits from Graphs and Tables
- 0/0 is indeterminate, not an answer of zero.
- What does “Continuity at an Input” mean?Continuity
- Agreement between a function value and its nearby limiting value.
- What important condition applies to continuity at an input?Continuity
- All three conditions—value, limit, and agreement—are required.
- What does “Jump Discontinuities” mean?Continuity
- A discontinuity caused by different finite left and right limits.
- What important condition applies to jump discontinuities?Continuity
- The assigned point value cannot force unequal one-sided limits to agree.