Change of Sign Failure (AQA A-Level Mathematics): Flashcards
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Change of sign failure
Change of sign failure
Method doesn't detect a root that exists
Why repeated roots cause failure
Why repeated roots cause failure
Function touches x-axis without crossing, no sign change
Example of repeated root function
Example of repeated root function
at
Other cause of change of sign failure
Other cause of change of sign failure
Discontinuous functions
Alternative to change of sign method (1)
Alternative to change of sign method (1)
Newton-Raphson
Alternative to change of sign method (2)
Alternative to change of sign method (2)
Fixed-point iteration
Requirement for change of sign method to work
Requirement for change of sign method to work
Function must be continuous in the interval
Example of discontinuity causing failure
Example of discontinuity causing failure
f(x) = rac{1}{x} has discontinuity at -axis
Multiple roots in interval, no sign change - why?
Multiple roots in interval, no sign change - why?
Both endpoints have same sign (both + or both -)
Can root exist if and same sign?
Can root exist if and same sign?
Yes, if function turns within interval (e.g., has turning point)