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Continuita

Continuita

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20 lug 20261 min read

Topic — Continuita.

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41

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22 linked atoms.

41 Continuità e discontinuità

  • x
  • Computing roots with Newton
  • Continuity at the junction point
  • Cube root of 10 with Newton
  • Definition of continuity
  • Determining the parameters for continuity
  • Elementary functions are continuous
  • Examples of classification
  • Function with no maximum on [0,1]
  • |x|
  • Newton exact for linear functions
  • Newton iteration for the reciprocal
  • Newton on x³−3x+1
  • Newton versus bisection and cases of failure
  • Parameters for continuity and differentiability
  • The bisection algorithm
  • The intermediate value theorem
  • The Newton-Raphson method
  • The three types of discontinuity
  • The zero theorem
  • Weierstrass’s theorem
  • Zero of x³−3x+1 with bisection

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  • Definition of continuity
  • Elementary functions are continuous
  • Continuity at the junction point
  • Determining the parameters for continuity
  • The three types of discontinuity
  • Examples of classification
  • Weierstrass's theorem
  • The intermediate value theorem
  • The zero theorem
  • The bisection algorithm
  • The Newton-Raphson method
  • Computing roots with Newton
  • Newton versus bisection and cases of failure
  • Newton on x³−3x+1
  • Newton iteration for the reciprocal
  • Cube root of 10 with Newton
  • Newton exact for linear functions
  • Classifying the discontinuity of |x|/x
  • Parameters for continuity and differentiability
  • Zero of x³−3x+1 with bisection
  • Function with no maximum on [0,1]
  • Limit and discontinuity of x/|x|