What value of c makes f(x)=(x²−9)/(x−3) for x≠3, and f(3)=c continuous?
Show a complete solution and verify with a second representation.
Unit 03 · Core Pathway
Continuity & Asymptotic Behavior
How do continuity conditions connect local behavior, global guarantees, and model reliability?
Khaemenes Academy · Calculus I
Core Practice
Continuity & Asymptotic Behavior · Show reasoning, notation, intervals, units, and corrections.
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Does a jump discontinuity have a two-sided limit?
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Why must continuity be checked before using IVT?
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Classify a finite hole in a graph.
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Why must continuity be checked before using IVT?
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Classify a finite hole in a graph.
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What does the Intermediate Value Theorem guarantee?
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List the three conditions for continuity at x=a.
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What does the Intermediate Value Theorem guarantee?
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A table approaches 4.999 from the left and 5.001 from the right. State the two-sided limit.
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Evaluate lim x→0 of sin x/x.
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What value of c makes f(x)=(x²−4)/(x−2) for x≠2, and f(2)=c continuous?
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Does a jump discontinuity have a two-sided limit?
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For f(x)=1/(x−3), identify the vertical asymptote.
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As x→∞, evaluate 5/x.
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Distinguish a vertical from a horizontal asymptote.
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