AQA A Level Maths: Pure复习笔记10.1.1 Change of Sign

Change of Sign

What does a change of sign mean?

  • sign change between f(a) to f(b) means there must be a root between a and b
  • When an equation cannot be solved using the usual analytical methods, we can use change of sign to find approximate solutions
  • We can say a root lies within a particular interval or is correct to a given accuracy
  • Bounds can be used to show a root is correct
  • Using sign change to find a root is only appropriate for continuous functions in a small interval

10.1.1-Change-of-Sign-Diagram-1

Exam Tip

  • Remember this will only work if the function is continuous and the interval is small enough.
  • Sign change questions may be part of bigger numerical methods questions.

Worked Example

10.1.1-Change-of-Sign-Example-Solution

 

 

 

 

 

 

转载自savemyexams

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