Limits and the Calculus Bridge flashcards

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What is approaching a value?Limits from Graphs and Algebra: The output approached as inputs approach a specified value.
What condition or caution matters when using approaching a value?Limits from Graphs and Algebra: A two-sided limit requires matching left and right limits.
What is removable discontinuities?Limits from Graphs and Algebra: A missing or mismatched function point with an existing finite limit.
What condition or caution matters when using removable discontinuities?Limits from Graphs and Algebra: The expression 0/0 is indeterminate, not zero.
What is continuity at a point?Continuity and End Behavior: Agreement of a defined function value with its two-sided limit.
What condition or caution matters when using continuity at a point?Continuity and End Behavior: A matching limit and function value are both required.
What is rational limits at infinity?Continuity and End Behavior: The limiting behavior of rational outputs as input magnitude grows.
What condition or caution matters when using rational limits at infinity?Continuity and End Behavior: A horizontal asymptote can be crossed at finite inputs.
What is average rate and secant lines?Rates of Change and the Calculus Bridge: The ratio of output change to input change over an interval.
What condition or caution matters when using average rate and secant lines?Rates of Change and the Calculus Bridge: Use output difference divided by input difference, not the reverse.
What is difference quotients and tangent rates?Rates of Change and the Calculus Bridge: A limiting secant slope defining instantaneous change.
What condition or caution matters when using difference quotients and tangent rates?Rates of Change and the Calculus Bridge: h approaches zero but is nonzero during quotient simplification.