Calculus I · Limits and Continuity · lesson
Two-Parameter Continuity Problems
Learn Two-Parameter Continuity Problems with plain-language explanations, guided examples, worked homework methods, interactive checks, and exam-style practice.
Where this chapter fits
Chapter 5: Continuity
Connect limits to function values, classify discontinuities, repair piecewise definitions, and use the Intermediate Value Theorem.
Reading lens: Do the limit, the function value, and the surrounding domain fit together at the point or across the interval? Keep that question in view while reading Two-Parameter Continuity Problems; the worked mathematics is evidence for the idea, not a substitute for it.
This page connects Choosing Parameters for Piecewise Continuity to Intermediate Value Theorem. Read the explanation first, predict each example’s next move, and only then compare the written solution.
Two conditions and two parameters
Solve a two-parameter continuity system
Choose and so that
is continuous at both and .
Show worked solution
At , continuity requires
At , continuity requires
Thus,
so
Use :
so
Therefore,
Source & rights
Original instruction with traceable references.
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