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Questions and Answers
A cusp is a type of discontinuity in a function.
A cusp is a type of discontinuity in a function.
False
The derivative of a function is defined at a cusp.
The derivative of a function is defined at a cusp.
False
A cusp is a point where a function is not continuous.
A cusp is a point where a function is not continuous.
False
A cusp is a type of singularity where the function is not defined.
A cusp is a type of singularity where the function is not defined.
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The existence of a cusp in a function does not affect the continuity of the function.
The existence of a cusp in a function does not affect the continuity of the function.
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The derivative of a function is always defined at a point where the function is continuous.
The derivative of a function is always defined at a point where the function is continuous.
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The limit as h→0 is used to find the slope of a function because Δx approaches infinity.
The limit as h→0 is used to find the slope of a function because Δx approaches infinity.
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A function can have a cusp at a point where its derivative is defined.
A function can have a cusp at a point where its derivative is defined.
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The existence of a cusp in a function implies that the function is not continuous at that point.
The existence of a cusp in a function implies that the function is not continuous at that point.
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The limit as h→0 is used to find the slope of a function because Δy approaches 0.
The limit as h→0 is used to find the slope of a function because Δy approaches 0.
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Study Notes
Continuity and Discontinuity
- A cusp is a type of discontinuity in a function.
- A cusp is a point where a function is not continuous.
- Despite this, the derivative of a function is still defined at a cusp.
Singularities
- A cusp is a type of singularity where the function is not defined.
Function Continuity
- The existence of a cusp in a function does not affect the overall continuity of the function.
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Description
Test your knowledge about cusps in functions, including their definition, relation to discontinuity, and effect on function continuity and derivatives.
