Questions and Answers
A cusp is a type of discontinuity in a function.
False
The derivative of a function is defined at a cusp.
False
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.
Signup and view all the answers
The existence of a cusp in a function does not affect the continuity of the function.
Signup and view all the answers
The derivative of a function is always defined at a point where the function is continuous.
Signup and view all the answers
The limit as h→0 is used to find the slope of a function because Δx approaches infinity.
Signup and view all the answers
A function can have a cusp at a point where its derivative is defined.
Signup and view all the answers
The existence of a cusp in a function implies that the function is not continuous at that point.
Signup and view all the answers
The limit as h→0 is used to find the slope of a function because Δy approaches 0.
Signup and view all the answers
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.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your knowledge about cusps in functions, including their definition, relation to discontinuity, and effect on function continuity and derivatives.